IP Final Report Group 5 P&C

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Reinsurance Pricing 08.18.2016

Integrated Project Group 5 P&C

Mentor: Sandip Kapadia

Students: Zijun Chen

Jiawen Wu

Citlalli Blanchet

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Table of content

1. Executive summary 4

2. Introduction to reinsurance 4

3. Quota Share 6

3.1 Loss Development 7

3.1.1 Chain Ladder method 7

3.1.2. Bornhuetter-Ferguson method (B-F method) 8

3.1.3 Trending 9

3.2 Premium Development 9

3.2.1 On-level Premium 9

3.2.2 Premium Trending 10

3.3 Loss Ratio 11

3.4 Loss Ratio Distribution fitting 12

3.5 Treaty Features 15

3.5.1. Sliding Scale Commission 16

3.5.2.Profit commission 16

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3.5.3.Loss Corridor 17

3.5.4 Flat ceding commission 17

4. Excess of Loss 17

4.1. Pricing methods of Excess of Loss reinsurance. 17

4.1.1. Experience rating 18

4.1.2. Exposure rating 19

4.2. Expected Loss cost. 21

5. Conclusion 21

6. Reference 23

7. Appendix 24

7.1 Statement of Intent 24

7.2 Project Charter 31

7.3 Minutes 41

7.4 Agenda 69

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1. Executive summary

Our objective is to build two models that price two types of reinsurance and evaluate the results.

The reinsurance contracts analyzed are for a book of business in General Liability. We will look at

Quota Share and Excess of Loss reinsurance contracts and take into consideration, profit,

commissions, and different layers for the Excess of Loss reinsurance.

2. Introduction

Reinsurance is the practice of insurers transferring portions of risk portfolios to other parties by

some form of agreement in order to reduce the likelihood of having to pay a large obligation

resulting from an insurance claim. By getting a reinsurance contract, the insurance company

reduces the risks associated with underwritten policies, it can also spread the risks across

alternative institutions.

In our project we are taking the position of a Reinsurance company. The line of business that we

are studying is General Liability which covers claims of bodily injury, physical injury, property

damage, and advertising injury. It is sold to protect the businesses against incidents that may occur

on the premises or at other locations where they conduct business.

A Quota Share reinsurance is a proportional contract where one or more reinsurance companies

take a stated percentage share of each policy that an insurer issues. The reinsurer will then receive

a fixed percentage of the premiums and will pay the stated percentage of claims. In addition the

reinsurer will allow a ceding commission to the insurer to cover the cost incurred by the insurer for

acquisition and administration.

Figure 2.1

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An Excess of Loss reinsurance is a non-proportional reinsurance in the sense that it will only pay

out if the total claims suffered by the insurer in a given period exceed a stated amount, which is

called “retention” or “priority”. We analyze it on a per occurrence basis and consider two different

contract layers: 3 million excess of 2 million and 4 million excess of 1 million. In the following

figure we can see that the premium ceded to the reinsurance company is an amount set at the

beginning of the contract.

Figure 2.2

The General Liability data used in this analysis was provided by our Mentor,

Mr. Kapadia, and correspond to a modified version of real data of an insurance company.

● Triangle of fifteen years of gross losses by accident year.

● Historical premium per year..

● Rate changes.

● Limit profiles.

● Increased Limit factors (ILF).

● Earned premium.

● Trend.

● Individual claims listing.

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Following we will describe the pricing methodologies for a Quota Share and an Excess of Loss

reinsurance.

3. Quota share

To price a Quota Share insurance we need to first take into consideration the historical loss ratios

projected to the treaty period. The loss ratio is the ratio of expected ultimate losses and the

adjusted historical premium. The expected ultimate losses is calculated using a Chain Ladder and

the Bornhuetter-Ferguson method (B-F method) and the adjusted historical premium needs to be

on leveled and trended using the parallelogram method. Then comes the decision that the ceding

company takes in terms of the percentage of losses retained and the type and amount of ceding

commission. The ceding commissions studied in this project are:

● Flat commission

● Sliding scale

● Profit commission

● Loss corridor commission.

For the purpose of comparing the different models of reinsurance in this project we will use the

Flat ceding commission.

The ceding commission will be set by the insurance company, but as reinsurers we need to

estimate a ceding commission that will consider the expected loss cost, expenses, brokerage fees

and the profit that we are willing to get for this contract.

Before committing to take the risk, the insurance company and the reinsurance company compare

the expected loss ratios that each of them calculated based on the historical gross losses and they

agree on the terms of the ceding commission.

For this model we had the following information available:

● A triangle of General Liability ground up losses with 15 years of experience.

● Earned premium.

● Historical Rate changes.

We have the following assumptions:

● Premium trending rate is 2%.

● Loss trending rate is 4%.

● No more loss development after 15 years.

● Interest rate do not change.

A more detailed explanation of the calculations follows.

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3.1 Loss development.

The first step of pricing a Quota Share reinsurance is to obtain the ultimate losses by accident year.

In order to do this, we use the Chain Ladder method and the Bornhuetter-Ferguson method (B-F

method).

3.1.1. Chain ladder method

This method operates under the assumption that patterns in claims activities in the past will

continue to be seen in the future. The ground up losses in the triangle represent the incremental

losses settled in the development year (column) for the given accident year (row).

a) Age-to-age factor

The age-to-age factor measures the changes of the development from one year to the next. It is

calculated by taking the ratio of reported loss of chosen year to the previous year. For each of the

age-to-age factors, we calculated different ways to obtain an average. We calculated the following

average types:

● Geometric average:

𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 = ∏ 𝑥𝑖

● Median average:

𝑀𝑒𝑑𝑖𝑎 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 = ∑ 𝑥𝑖

𝑛−2

𝑖=1

− min(𝑥𝑖) − max (𝑥𝑖)

● Volume weighted average:

𝑉𝑜𝑙𝑢𝑚𝑒 𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 =𝛴(𝐿𝑜𝑠𝑠𝑒𝑠 𝑎𝑡 𝑛 + 12, 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 5 𝑦𝑒𝑎𝑟𝑠)

𝛴(𝐿𝑜𝑠𝑠𝑒𝑠 𝑎𝑡 𝑛, 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 5 𝑦𝑒𝑎𝑟𝑠)

● Simple average:

𝑆𝑖𝑚𝑝𝑙𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 =∑ 𝑥

𝑛

We did not observe a significant variation in the prior methods of obtaining the average of the

development factors. So, we decided to use the simple average as is is easier to interpret. We

assumed that we won’t have loss development after 15 years then the tail age-to-age factor is 1.

We observed that even though we were working with cumulative ground up losses there were

some development years that had loss development factors less than one. This can happen due to

the fact that the data includes some salvage and subrogation. This behavior was mostly present in

older years and at more than 48 months of development. We decided to include them in the

selected simple average to reflect this behavior.

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Figure 3.1

b) Estimating Ultimate loss amounts

The cumulative development factors (CDF) are used to measure changes of loss for each policy

from certain accident year to ultimate loss. The Chain Ladder method calculates them for each

accident year as the multiplication of the Loss development factors after the last period that the

data was observed. The quantity further used in this analysis is the percentage of loss reported that

is obtained as 1/CDF.

Figure 3.2

3.1.2. Bornhuetter-Ferguson method (B-F method)

The B-F method is used to calculate expected ultimate loss. Compared to the Chain Ladder

method, B-F method it can avoid overreaction when unusual values appear. It is based on reported

loss and the projected to ultimate loss calculated by the Chain Ladder method. As mentiones

above,

𝑈𝑛𝑟𝑒𝑝𝑜𝑟𝑡𝑒𝑑 𝐿𝑜𝑠𝑠 = 𝑃𝑟𝑜𝑗𝑒𝑐𝑡𝑒𝑑 𝑡𝑜 𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝐿𝑜𝑠𝑠 ∗ (1 −1

𝐶𝐷𝐹)

Then the expected ultimate loss is the sum of reported loss and unreported loss.

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3.1.3. Trending

After obtaining the Ultimate losses per accident year we need to trend them. We assumed a loss

trend of 4% per year. So we measured the length of trend from the average date in the

corresponding accident year to the the average current date 07/01/2016. The adjusted ultimate loss

is calculated as follows:

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝐿𝑜𝑠𝑠 = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝐿𝑜𝑠𝑠 ∗ (1 + .04)𝑙𝑒𝑛𝑔𝑡ℎ

3.2 Premium development

Steps

3.2.1 On-level premium

The parallelogram method assumes that premiums are written evenly throughout the time period, it

involves adjusting the aggregated historical premium by an average factor to put the premium on-

level. We need to consider historical rate changes when we on-level the premiums. We had the

following historical rate changes per year:

Year Rate Change

2006 -3.0%

2007 -4.0%

2008 -5.0%

2009 -4.0%

2010 2.0%

2011 2.0%

2012 -0.5%

2013 -2.0%

2014 1.0%

2015 -1.0%

Figure 3.3

The objective of the parallelogram method is to replace the average rate level for a given historical

year with the current rate level. The steps for the parallelogram method are as follows:

1. Determine the timing and amount of the rate changes during the experience period.

2. Calculate the portion of the year’s earned premium corresponding to each rate level group.

3. Calculate the cumulative rate level index for each rate level group.

4. Calculate the weighted average cumulative rate level for each year.

5. Calculate the on-level factor as the ratio of the current cumulative rate level level index and the

average cumulative rate level index for the appropriate year.

6. Apply the on-level factor to the earned premium for the appropriate year.

To view the rate changes in a graphical format as in figure 3.4 assume that rate changes only

impact policies written on or after the effective date therefore the rate change are represented by a

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diagonal line, the slope of the line depends on the term of the policy for the purpose of this

analysis they are one year policies.

Figure 3.4

The on level factor formula is as follows:

𝑂𝑛 − 𝑙𝑒𝑣𝑒𝑙 𝐹𝑎𝑐𝑡𝑜𝑟 =𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐶𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒 𝐿𝑒𝑣𝑒𝑙 𝐼𝑛𝑑𝑒𝑥

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑒 𝐿𝑒𝑣𝑒𝑙 𝑖𝑛𝑑𝑒𝑥 𝑓𝑜𝑟 ℎ𝑖𝑠𝑡𝑜𝑟𝑖𝑐𝑎𝑙 𝑃𝑒𝑟𝑖𝑜𝑑

The numerator considers the most recent cumulative rate level index from Step 3. The denominator

is the result of Step 4.

3.2.2. Premium trending

We selected a one-step trending approach. The premium trend that we selected is 2%. The selected

trend factor is used to adjust the historical premium to the expected levels. The trend period is

typically measured as the length of time from the average date of policies with premium earned

during the historical period to the average written date for policies that will be in effect during the

time the rates will be in effect in this case 07/01/2016.

The trending factor is defined as follows:

𝑇𝑟𝑒𝑛𝑑𝑖𝑛𝑔 𝑓𝑎𝑐𝑡𝑜𝑟 = (1 + .02)𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡𝑟𝑒𝑛𝑑

Each on-level premium is then multiplied by the trending factor to get the adjusted ultimate

premium. The following is a summary table for the premium calculation.

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Figure 3.5

3.3 Loss Ratio

After getting the adjusted ultimate loss and the on-leveled and trended premium for each accident

year, we get the loss ratio as follows:

𝐿𝑜𝑠𝑠 𝑟𝑎𝑡𝑖𝑜 =𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝐿𝑜𝑠𝑠

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚

We select the expected loss ratio as the average loss ratio of the 15 years of experience. This gives

is a 54% Loss ratio.

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Figure 3.6

3.4 Loss Ratio Distribution fitting

Based on all the analysis above, now we have 15 years of historical loss ratios. As an exercise we

wanted to get more information about the distribution of the loss ratio of this book of business.

With the information available we have 15 years of experience.

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AY Loss Ratio

2001 61.9% 2002 54.9% 2003 53.3% 2004 45.4% 2005 52.8% 2006 29.0% 2007 60.5% 2008 59.1% 2009 43.9% 2010 54.5% 2011 40.8% 2012 58.6% 2013 64.8% 2014 63.9% 2015 66.7%

Figure 3.7

We use @risk software to fit a distribution to the loss ratio. Then based on the Akaike information

criterion (AIC) criteria we compared the distributions and choose the one that had the lowest AIC

criterion.

Note: The Akaike information criterion (AIC) is a measure of the relative quality of statistical

models for a given set of data. Given a collection of models for the data, AIC estimates the quality

of each model, relative to each of the other models. Hence, AIC provides a means for model

selection.

The selected distribution is a Weibull distribution. Figure 3.8, shows it.

https://en.wikipedia.org/wiki/Statistical_model

https://en.wikipedia.org/wiki/Statistical_model

https://en.wikipedia.org/wiki/Model_selection



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Figure 3.8

We found that the Weibull distribution is the best distribution to describe our 15 years historical

loss ratio data. But the problem for this distribution is that this distribution has a light tail, which is

not good enough to predict some extreme events. The reason behind this may be that our historical

data size is not large enough, so we need to add one more extreme event in our dataset. We added

one observation of 125% loss ratio to the 15 observations previously used.

After adding this new observation we fitted the new distribution again and using the sale AIC

criteria, we found that the Log-Logistic distribution is a good fit.

Figure 3.9

The second best distribution is a Pearson5 Distribution. The Log-Logistic distribution has similar

shape to the log-normal distribution but has heavier tails. In this analysis we can see that the

Pearson5 distribution has a heavier tail than the Log-Logistic distribution. Even though that is the

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case we would recommend the use of the Log-Logistic because its cumulative distribution can be

written in closed form and it is known for it uses in economics and to measure survival analysis.

We found this analysis very interesting and we got motivated to further investigate about the

sensitivity of the pricing methods to the loss ratio and how this distribution can be used in

replacing or complementing the Increased Limit Factors from the industry used in the Excess of

Loss pricing analysis.

3.5 Treaty Features

An important part of pricing a Quota Share reinsurance is to take into consideration the ceding

commission. For our final analysis we used a Flat ceding commission but we also studied different

types. Following are the description and examples of the commissions that can be considered in

this type of reinsurance.

3.5.1. Sliding Scale Commission

When there are disagreements between insurer and reinsurer, we may need to use the sliding scale

commission to keep a balance between the insurer and reinsurer.

Sliding scale commission ensures that the actual rate payable is directly related to the loss ratio,

which means more commission in good years and lower commission in bad years.

A common adjustable feature is the “sliding scale” commission. A sliding scale commission is a

percent of premium paid by the reinsurer to the ceding company which “slides” with the actual

loss experience, subject to set minimum and maximum amounts.

We made 1,000 loss ratio simulations. In the calculation of the sliding scale commision, for each

loss ratio simulated, we need to determine in which range the loss ratio falls into: below 50%, 50%

- 60%, or above 60%. And then we apply the sliding scale to these loss ratio, and calculate the new

average value of the 1,000 data, which is considered as the expected sliding commission.

Figure 3.10

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3.5.2.Profit commission

A profit commission subtracts the actual loss ratio, ceding commission and a “margin” for expenses from the treaty premium and returns a percent of this as additional commission.

Profit commission is the reward given to the insurance company for providing profitable business, by the reinsurer.

Here is the formula:

Profit = Premium – Loss - Commission-Reinsurer’s margin

Profit Commission is payable in addition to ceding commission and applicable to proportional treaties and rarely seen in Non Proportional treaties.

Figure 3.11

3.5.3.Loss Corridor

The Insurance company will reassume a portion of the reinsurer's liability if the loss ratio exceeds a certain amount.

A loss corridor provides that the ceding company will reassume a portion of the reinsurer’s liability if the loss ratio exceeds a certain amount.

In our case the corridor is 25% of the Loss ratio layer from 65% to 75%.

Figure 3.12

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3.5.4 Flat ceding commission

For the purpose of our project we will price a Quota Share insurance assuming a 25% of ceded

losses. Meaning that the insurance company will retain 75% of the losses.

For the purpose of the analysis we calculated a flat ceding commission taking into the following paraments:

● Expected loss ratio: 54% ● Brokerage fee: 2% ● Profit: 10%

The calculation of the Flat ceding commision is as follows:

𝐶𝑒𝑑𝑖𝑛𝑔 𝐶𝑜𝑚𝑚𝑖𝑠𝑖𝑜𝑛 = 1 − 𝑃𝑟𝑜𝑓𝑖𝑡 − 𝐸𝑥𝑝𝑒𝑛𝑠𝑒 − 𝐵𝑟𝑜𝑘𝑒𝑟𝑎𝑔𝑒 𝐹𝑒𝑒 − 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠 𝑐𝑜𝑠𝑡

Considering these parameters we obtained a Flat ceding commission of 29%.

Expected

Loss Cost

$ 6,786,592

Brokerage

Fee

$251,350

Expenses $628,376

Ceding

Commission

$3,644,447

Profit $1,256,752

Premium

ceded

$12,567,516

Figure 3.13

4. Excess of Loss.

4.1. Pricing methods of Excess of Loss reinsurance.

Exposure and experience rating are the most prevalent approaches to pricing excess of loss

reinsurance contracts. They are frequently used together in a form of a credibility-weighted

average to calculate the expected loss cost.

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As mentioned before we consider two different layers for an Excess of Loss reinsurance:

•3 x 2 Three million excess of two million.

•4 x 1 Four million excess of one million.

The assumptions used for both Experience and Exposure methods are:

•Exposure trend for Premiums 2%.

•Historical rate changes.

•Loss trend 4%.

•A tail factor 10% to the Loss Development Factor on each layer.

4.1.1. Experience rating

The basic idea of experience rating is that the historical experience, adjusted properly, is the best

predictor of future expectations. Experience rating uses historical losses of the ceding company. As

we will be able to see in the case of the two layers studied in the project, there could be the case

that no losses will fall in the layer and this will make the calculations of the expected loss cost less

reliable.

The information used in this analysis is on a per claim basis. The premium used was the one used

in the Quota Share pricing, on leveled and trended. Below are the calculation’s steps.

1. Individual loss claims. Each of the ground up losses is trended to the future average date of loss in

this case is 7/1/2016. The resulting loss is applied to the reinsurance layer.

2. For each claim calculate the loss corresponding to the layer to price and aggregate them by

accident year.

3. Aggregated losses in the layer are then developed to ultimate.

4. Historical premium is adjusted for rate changes to the prospective premium level.

5. The loss cost of the layer by year is calculated by dividing the ultimate trended losses in the layer

by the corresponding adjusted premium.

6. Then we calculate the average of the loss cost between the most recent years, 2006 to 2016.

7. The reinsurance rate is developed by loading the loss cost for the reinsurer’s expense and profit.

In our analysis we can see that for the layer of 3 x 2 there are some years that do not have any

losses falling in this layer. Whereas for the layer 4 x 2 all the accident years considered, from 2006

to 2015 have losses. Figure 4.1 shows the resulting Loss cost per layer.

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Layer Experience

Loss cost

3 x 2 5.62%

4 x 1 17.96%

Figure 4.1

It seems that in the layer of 4x1 presents more losses in the layer than the 3 x 2 Excess of Loss

reinsurance. In this case, we could say that is for this particular layer the Experience method is

more “reliable”.

In the appendix we show a summary table for both layers.

4.1.2. Exposure rating

The exposure rating method relies on a current snapshot of the policies subject to the reinsurance

contract. This snapshot will include some measure of the percentage of premium exposing the

reinsurance contract, usually called the “Limit profile”, and an estimate of the gross loss, before

reinsurance, for such policies. To perform an exposure rating we require a severity distribution,

from which we can get the Increased Limit Factors (ILFs). We obtained these ILFs based on the

industry benchmark provided by our mentor. The objective of the exposure rating method is to

estimate the proportion of the loss for the underlying policy that is expected in the Excess of Loss

layer.

Exposure rating is suitable for those companies who have a book of business similar to the

industry’s, for companies lacking data or having not reliable data. In this case, exposure rating

might be the best way to obtain the expected loss cost since experience rating may not be very

reliable. In this method all is based on in-force data without relying on historical one.

The ILFs are defined as:

𝐼𝐿𝐹 =𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐶𝑜𝑠𝑡 𝑎𝑡 𝑡ℎ𝑒 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑝𝑜𝑙𝑖𝑐𝑦 𝑙𝑖𝑚𝑖𝑡

𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐶𝑜𝑠𝑡 𝑎𝑡 𝑡ℎ𝑒 𝐵𝑎𝑠𝑖𝑐 𝐿𝑖𝑚𝑖𝑡

The Loss ratio is defined as the gross loss divided by the gross premium. The loss cost can be

calculated using the loss ratio as in the following formula:

𝐿𝑜𝑠𝑠 𝑐𝑜𝑠𝑡 =𝐺𝑟𝑜𝑠𝑠 𝐿𝑜𝑠𝑠

𝐺𝑟𝑜𝑠𝑠 𝑃𝑟𝑒𝑚𝑖𝑢𝑚×

𝐶𝑒𝑑𝑒𝑑 𝐿𝑜𝑠𝑠

𝐺𝑟𝑜𝑠𝑠 𝑃𝑟𝑒𝑚𝑖𝑢𝑚

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One way of calculating the loss cost is first calculate the Base premium that is the premium of the

basic limit. We use the inforce premium by policy limit. The Base premium is calculated as

follows:

𝐵𝑎𝑠𝑒 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 =𝑃𝑟𝑒𝑚𝑖𝑢𝑚 𝑜𝑓 𝑐𝑒𝑟𝑡𝑎𝑖𝑛 𝑝𝑜𝑙𝑖𝑐𝑦 𝑙𝑖𝑚𝑖𝑡

𝐼𝐿𝐹 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑙𝑖𝑐𝑦 𝑙𝑖𝑚𝑖𝑡

Then to get the premium corresponding to the losses in the layer of interest, we multiply the Base

premium by the difference of the upper and lower limit’s ILFs.

𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟 = (𝐵𝑎𝑠𝑒 𝑝𝑟𝑒𝑚𝑖𝑢𝑚) ∗ (𝑈𝑝𝑝𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 𝐼𝐿𝐹 − 𝐿𝑜𝑤𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 𝐼𝐿𝐹)

We then multiply the adjusted premium of the layer to the expected loss ratio. To obtain the

expected losses in the layer per policy limit.

Part of the Exposure analysis is to take into consideration the ceding company’s limit profile. We

obtain this by dividing each policy limit in force premium by the total inforce premium. Once we

have the limit profile we multiply each of the expected losses by limit in the layer times its

corresponding limit profile and then we add them all to obtain the expected loss cost.

The expected loss cost for the layer 4x1 is 1.66% and for the layer 3x2 is 0.65%.

Figure 4.2

21

4.2. Expected Loss cost.

After calculating the experience and exposure loss cost we combine them in a form of credibility

giving both methods the same weight.

Figure 4.3

5. Conclusion

Based on the analysis on the Quota Share and the Excess of Loss pricing , now we can give a final

review and comparison for these two different reinsurance contracts.

As part of the reinsurance contract our company will receive part of the premium from the ceding

company and then we will take part of the risk involved. The main difference of these two types of

reinsurance contracts is how to determine the part of the risk assumed.

Here is a graph to show this concept:

Figure 5.1

Assuming the percentage ceded in the case of the Quota Share and the limits in the case of the

Excess of loss, we can discuss the final outcome for these two methods:

22

Figure 5.2

In summary, we have described the methods to price a Quota Share and an Excess of Loss

reinsurance. We described the assumptions we made and how given a set percentage of profit we

came up with a given ceded premium. For pricing purposes this is just a reference for the

reinsurance company. In a real life scenario, the insurance company and the market will dictate the

terms of the contract. This is when the different types of ceding commissions come into play as a

tool for the reinsurance company to negotiate with the ceding company if their calculations of

expected losses differ. There are many metrics to determine whether to write a treaty: loss ratio,

dollars of profit, ceded premium, cost of capital, ROI to name a few. In this case we base our

recommendations on profit.

We assume 10% of profit for each contract. As we can see in Figure 5.2 the expected loss for the

Quota Share is just 30% above the one expected for the 4x1 Excess of Loss reinsurance, and the

profit is 87% higher that the 4x1 Excess of Loss contract. For this reason we come to the

conclusion that recommending a Quota Share reinsurance is a reasonable start in the negotiations.

For the two layers of the Excess of Loss reinsurance. We found that the layer of 3x2 had years

where no data was available when calculation the Experience rating and the expected loss cost

calculated may not be very reliable due to the lack of data. For this reason in the case that the

insurance company may be interested in an Excess of Loss reinsurance we will recommend to

quote a 4x1 layer. In general there are many factors that determine which kind of reinsurance the

ceding company selects. For example, It can depend on the resources to write business to ensure

profitability or how much surplus relief it needs.

23

6. Reference

Ana J. Mata and Mark A. Verheyen (2005), An Improved Method for Experience Rating

Reinsurance Treaties using Exposure Rating Techniques

David R. Clark, (2014), Basics of Reinsurance Pricing, Actuarial Study Note

David R. Clark, (2007), Introduction to Experience Rating, Casualty Actuarial Society

Reinsurance Pricing Seminar

Michael Petrocik, (2006), De-Mystifying Reinsurance Pricing, STRIMA Conference

Baton Rouge, LA

Halina Smosna, (2008), Introduction to Exposure Rating, CAS Ratemaking Seminar Boston

Mark Flower (Chairman); Ian Cook; Craig Divitt; Visesh Gosrani; Andrew Gray; Gillian James; Gurpreet Johal; Mark Julian; Lawrence Lee; David Maneval; Roger Massey, (2006), Reinsurance Pricing: Practical issues & Considerations,

Kevin Hilferty, (2013), Property And Casualty Exposure Rating

Li Zhu, (2011), Introduction to Increased Limit Factors, RPM Basic Ratemaking Workshop

Geoff Werner and Claudine Modlin, (2010), Basic Ratemaking

24

7. Appendix

7.1 Statement of Intention

Property/Casualty

Reinsurance Pricing

Statement of Intention -

Group #5

Project Title

Property/Casualty Pricing for Quota Share and Excess of Loss reinsurance.

Team Members and Contact Information

Name

E-mail

Phone Number Mentor Sandip Kapadia [email protected] (973) 490 - 6103

Supervisors Noor Rajah

Lina Xu

[email protected]

(212) 851 - 9961

TA Ehtesham Malik [email protected] Group Members Zijun Chen [email protected] (646) 830 - 4003

Jiawen Wu [email protected] (646) 830 - 4506

Citlalli Blanchet [email protected] (917)714 - 0356

mailto:[email protected]

https://courseworks2.columbia.edu/courses/7465/users/246







25

Abstract

Reinsurance is the practice of insurers transferring portions of risk portfolios to other parties by some

form of agreement in order to reduce the likelihood of having to pay a large obligation resulting from an

insurance claim. The intent of reinsurance is for an insurance company to reduce the risks associated with

underwritten policies by spreading risks across alternative institutions.

In our project we are taking the position of a Reinsurance company. We are going to analyze a General

Liability insurance. A General Liability insurance covers claims of bodily injury, physical injury,

property damage, and advertising injury. It is sold to protect the businesses against incidents that may

occur on the premises or at other locations where they conduct business.

26

Our objective is to come up with the best reinsurance structure for this book of business. We will

look at

Quota Share and Excess of Loss reinsurance contracts. We will take in to consideration, profit,

commissions, and different layers for the Excess of Loss reinsurance. We plan to include sensitivity

analysis as well as a detail list of all the assumptions needed to come up with the recommended rates per

type of contact.

Our project will include the following phases:

1. Data analysis: In this phase we will work on performing an exploratory analysis of the data,

understand its structure and come up with the assumptions needed. During this phase we are also going to

study the claim development methodologies as well as on leveling of premiums and trending both

premiums and losses. The objective of this phase is to come up with and Ultimate loss and an estimated

loss ratio.

2. Loss cost analysis: In this phase we plan to use the loss ratio of the prior phase and we are going

to perform an Exposure and an Experience rating analysis. We will also add some simulations all this with

the objective of obtaining the most “accurate” projected loss cost.

3. Pricing analysis: Use the projected loss cost to calculate for example for the Quota Share

reinsurance the ceding commission to get this book of business profitable. We will analyze different limit

scenarios for the Excess of Loss reinsurance. We will consider the possibility of adding treaty features and

perform a sensitivity analysis with the objective of giving a profitable rate for our reinsurance company.

Initial Project Milestones and Deliverables

We are meeting with our mentor on a weekly basis. Prior to each meeting we will prepare a meeting agenda.

We are currently in Phase 1 of our project. Our mentor has given us a list to literature to read related to

pricing reinsurance contracts. We are in the process of getting data. Our mentor kindly has offered to provide

us a dataset that most likely will include Loss experience, premium, expenses, of individual claims and

some policy listings. In the meantime, we are reviewing the recommended literature and we plan to discuss

any issues or exercises that will help us to get a better understanding of the theoretical procedures of the

project.

27

Followed by each or our weekly meeting we will prepare the weekly deliverables. These include agenda,

meeting minutes and a video update.

The key deliverables for the project include a statement of intent (week 3), a project charter (week 4), a

midterm presentation (week 7), a final report (week 12), and a final presentation (week 12).

28

Proposed Learning Outcomes

Analytical Skills

With the help of our mentor we are looking forward to understanding the assumptions needed to come

up with a model as close as possible to a real life one. To do this we will need to understand our data

and its structure. Also for the pricing phase we will need to understand what factors are needed to be

modified in order to give a sensitivity analysis and finally come up with a profitable reinsurance rate.

Technical Knowledge

With the guidance of our mentor and by performing extensive research in this topic, we will integrate

different tools from statistics, mathematics, and reinsurance theory. For example in the Data analysis

phase we can use R to come up with descriptive statistics. We are also planning to use @Risk to fit a

distribution to the expected losses data. We will use Excel to consolidate our analysis and have a user

friendly interphase to perform the sensitivity analysis.

Business Skills

Working on this project as a team we believe that will help us develop our business skills. For example

we need to coordinate efforts to come up with all the weekly deliverables. We rotate and divide work

so we all collaborate in a balance way and we help each ot her understand the project’s objectives a

theory behind it. We will practice our presentation skills by preparing our weekly video update and by

presenting our work progress to our mentor and project supervisors.

29

Oral Communication and Writing Skills

On a weekly basis we prepare an agenda, and the require deliverables for our project. We also need to

communicate in a professional way with our mentor and supervisors. We are planning on presenting

our project in the most professional manner. Our intention is to give pricing advice in the most

comprehensive way possible as we were talking to our insurance clients.

30

Project Plan

Week Project Progress Project Goals

Week 1: May 23 Complete To be familiar with project guidlines

Week 2: May 30 Complete Introductions/Project overview

Project Plan Due

Week 3: June 6 Complete Statement of Intent Due

Week 4: June 13

Definition of project phases

Read papers Project Charter Due

Week 5: June 20

Wrapped up dues. Analysis of

Week 6: June 27 Data analysis and start Loss cost

Week 7: July 3

Loss cost phase

Week 8: July 10

Midterm presentation. Preparation

Week 9: July 18

Midterm presentation

Week 10: July 25

Pricing Analysis

Week 11: Aug 1

Pricing Analysis

Sensitivity Analysis

Week 12: Aug 8

Prepare Final presentation

Week 12: Aug 15

Mock of final presentation

Week 12: Aug 25 Final presentation

Readings:

1 Basics of Reinsurance Pricing. David R. Clark, FCAS. Retrieved from

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwipq6kzZ_NAhWHpB4

KHcLpDdUQFggeMAA&url=https%3A%2F%2Fwww.soa.org%2Ffiles%2Fedu%2Fedu-2014-exam-at-study-

note-basics-rein.pdf&usg=AFQjCNGwn-OHg__Zb2FPO3nlj4XqVCI8cw&sig2=mLtfJhKumnMDJgePqXp8XQ

2. Reinsurance Pricing: Practical Issues and Considetations. 2008 GIRO “Reinsurance Matters” Working party

Mark Flower, Ian Cook, Craig Divitt, Visesh Gosrani, Andrew Gray, Gillian James, Gurpreet Johal, Mark Julian,

Lawrence Lee, David Maneval, Roger Massey.

https://www.google.com/url?sa=t&rct=j&q&esrc=s&source=web&cd=1&ved=0ahUKEwipq6kzZ_NAhWHpB4KHcLpDdUQFggeMAA&url=https%3A%2F%2Fwww.soa.org%2Ffiles%2Fedu%2Fedu-2014-exam-at-study-note-basics-rein.pdf&usg=AFQjCNGwn-OHg__Zb2FPO3nlj4XqVCI8cw&sig2=mLtfJhKumnMDJgePqXp8XQ




31

7.2 Project Charter

Property/Casualty Reinsurance Pricing Study

Project Charter

Group #5

Project Title

Property/Casualty Pricing for Quota Share and Excess of Loss reinsurance.

Team Members and Contact Information

Name

E-mail

Phone Number Mentor Sandip Kapadia [email protected] (973) 490 - 6103

Supervisors Noor Rajah

Lina Xu

[email protected]

(212) 851 - 9961

TA Ehtesham Malik [email protected] Group Members Zijun Chen [email protected] (646) 830 - 4003

Jiawen Wu [email protected] (646) 830 - 4506

Citlalli Blanchet [email protected] (917)714 - 0356

Abstract

Reinsurance is the practice of insurers transferring portions of risk portfolios to other parties by some form









32

of agreement in order to reduce the likelihood of having to pay a large obligation resulting from an

insurance claim. The intent of reinsurance is for an insurance company to reduce the risks associated with

underwritten policies by spreading risks across alternative institutions.

In our project we are taking the position of a Reinsurance company. We are going to analyze a General

Liability insurance. A General Liability insurance covers claims of bodily injury, physical injury, property

damage, and advertising injury. It is sold to protect the businesses against incidents that may occur on the

premises or at other locations where they conduct business.

We will work on a pricing analysis for a Quota Share and an Excess of Loss reinsurance contracts with the

objective to maximize the profit margins based on this book of business. A Quota Share reinsurance is a

proportional contract where one or more reinsurers take a stated percentage share of each policy that an

insurer issues. The reinsurer will then receive a fixed percentage of the premiums and will pay the stated

33

percentage of claims. In addition the reinsurer will allow a ceding commission to the insurer to cover the cost

incurred by the insurer for acquisition and

administration.

An Excess of Loss reinsurance is a non-proportional reinsurance in the sense that it will only pay out if

the total claims suffered by the insurer in a given period exceed a stated amount, which is called

“retention” or “priority”. We are going to analyze it on a per risk basis.

Scope and Objectives

Our objective is to come up with the best reinsurance structure for this book of business. We will look at

Quota Share and Excess of Loss reinsurance contracts. We will take in to consideration, profit, commissions, and different layers for the Excess of Loss reinsurance. We plan to include sensitivity analysis as well as a detail list of all the assumptions needed to come up with the recommended rates per type of contact.

Our project will include the following phases:

1. Data analysis: In this phase we will work on performing an exploratory analysis of the data, understand its structure and come up with the assumptions needed. During this phase we are also going to study the claim development methodologies as well as on leveling of premiums and trending both premiums and losses. The objective of this phase is to come up with and Ultimate loss and an estimated loss ratio.

2. Loss cost analysis: In this phase we plan to use the loss ratio of the prior phase and we are going to perform an Exposure and an Experience rating analysis .We will also add some simulations all this with the objective of obtaining the most “accurate” projected loss cost.

3. Pricing analysis: Use the projected loss cost to calculate for example for the Quota Share reinsurance the ceding commission to get this book of business profitable. We will analyze different limit scenarios for the Excess of Loss reinsurance. We will consider the possibility of adding treaty features and perform a sensitivity analysis with the objective of giving a profitable rate for our reinsurance company.

Approach and Threshold for Project Success

34

We got the following data for a GL line of business: A triangle of the Ground up reported losses and

LAE as of 12/31/2015. For years 2001 to 2015 and experience of 15 years;

We have GL individual Losses for claims that exceeded a $500,000 limit; and we also have available premium listings based on different GL limits.

Some of the techniques that we are planning to implement are:

In the loss ratio calculation we are going to determine the projected ultimate losses by using the

ground up losses triangle and the Bornhuetter -Ferguson (B-F) Technique.

For reinsurance pricing we will perform an Exposure rating technique using an Increase Limit

Factors (ILF) method, and an Experience rating technique.

35

We will fit a curve to the expected loss ratio for a Quota Share and to the selected loss cost for the XL. We may use @Risk and R to fit and select the most appropriate loss distribution that will describe them.

We will simulate the loss ratio and the selected loss cost to help us come up with suggested margins on negotiations while we consider treaty features.

Assumptions and Constraints

We will base our calculations on an Accident Year basis. For this we will consider the date of loss field in

the data set.

Although we will identify the assumptions once we start a more detailed analysis of the data. We consider that we will need to define them for the following steps on the project:

Trends.

Ceding commissions.

Expenses.

On-leveling the premium.

Adjustments for historical rate changes.

Determine the reinsurance treaty features.

Decide if we are going to base our analysis on the most recent data or t he whole history.

We may encounter some constraints in the simulation and curve fitting process since we lack a large amount of exposure years.

Initial Project Milestones and Deliverables

We are meeting with our mentor on a weekly basis. Prior to each meeting we will prepare a meeting

36

agenda. We are currently in Phase 1 of our project. Our mentor has given us a list to literature to read related to pricing reinsurance contracts. We got the data, that our mentor kindly provided. We continue reviewing the recommended literature and we plan to discuss any issues or exercises that will help us to get a better understanding of the theoretical procedures of the project. We will start with a Loss development analysis using the B-F method.

Followed by each or our weekly meeting we will prepare the weekly deliverables. These include agenda, meeting minutes and a video update.

37

The key deliverables for the project include a statement of intent (week 3), a project charter (week 4), a

midterm presentation (week 7), a final report (week 12), and a final presentation (week 12).

Proposed Learning Outcomes

Analytical Skills

With the help of our mentor we are looking forward to understanding the assumptions needed to come up

with a model as close as possible to a real life one. To do this we will need to understand our data and its

structure. Also for the pricing phase we will need to understand what factors are needed to be modified in

order to give a sensitivity analysis and finally come up with a profitable reinsurance rate.

Technical Knowledge

With the guidance of our mentor and by performing extensive research in this topic, we will integrate different

tools from statistics, mathematics, and reinsurance theory. For example in the Data analysis phase we can use R

to come up with descriptive statistics. We are also planning to use @Risk to fit a distribution to the expected

losses data. We will use Excel to consolidate our analysis and have a user friendly interphase to perform the

sensitivity analysis.

Business Skills

Working on this project as a team we believe that will help us develop our business skills. For example we

need to coordinate efforts to come up with all the weekly deliverables. We rotate and divide work so we all

collaborate in a balance way and we help each ot her understand the project’s objectives a theory behind it.

We will practice our presentation skills by preparing our weekly video update and by presenting our work

progress to our mentor and project supervisors.

Oral Communication and Writing Skills

On a weekly basis we prepare an agenda, and the require deliverables for our project. We also need to

38

communicate in a professional way with our mentor and supervisors. We are planning on presenting our

project in the most professional manner. Our intention is to give pricing advice in the most comprehensive

way possible as we were talking to our insurance clients.

39

Project Plan

Week Project Progress Project Goals

Week 1: May 23 Complete To be familiar with project guidlines

Week 2: May 30 Complete Introductions/Project overview

Project Plan Due

Week 3: June 6 Complete Statement of Intent Due

Week 4: June 13

Complete

Definition of project phases

Read papers . Project Charter Due .

Start Loss development analysis.

Week 5: June 20

Wrapped up dues. Exercises

discussion.

Week 6: June 27

Data analysis and start Loss cost

Week 7: July 3

Loss cost phase

Week 8: July 10

Midterm presentation. Preparation

Week 9: July 18

Midterm presentation

Week 10: July 25

Pricing Analysis

Week 11: Aug 1

Pricing Analysis

Sensitivity Analysis

Week 12: Aug 8

Prepare Final presentation

Week 12: Aug 15

Mock of final presentation

Week 12: Aug 25

Final presentation

Readings:

1 Basics of Reinsurance Pricing. David R. Clark, FCAS. Retrieved from

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwipq6kzZ_

NAhWHpB4

KHcLpDdUQFggeMAA&url=https%3A%2F%2Fwww.soa.org%2Ffiles%2Fedu%2Fedu-2014-

exam-at-study- note-basics-rein.pdf&usg=AFQjCNGwn-

OHg__Zb2FPO3nlj4XqVCI8cw&sig2=mLtfJhKumnMDJgePqXp8XQ

2. Reinsurance Pricing: Practical Issues and Considetations. 2008 GIRO “Reinsurance Matters”

Working party Mark Flower, Ian Cook, Craig Divitt, Visesh Gosrani, Andrew Gray, Gillian

James, Gurpreet Johal, Mark Julian, Lawrence Lee, David Maneval, Roger Massey.







40

3. 2011 RPM Basic Ratemaking workshop. Session 3: Introduction to increased

Limit factors. Li Zhu, FCAS, MAAA.

4. De-Mystifying Reinsurance Pricing. STRIMA conference Boston Rouge, LA September 26 2006.

Michael Petrocik FCAS, MAAA.

41

7.3 Minutes

Minutes of the Fifth Group Meeting of Integrated Project

Held on Thursday, 2 June 2016

12:00 a.m. at Science and

Engineering Library

Name Absent

Mentor Kapadia Sandip

Lina Xu TA Ehtesham Malik Student Citlalli Blanchet

Jiawen Wu

Zijun Chen

1. Students’ Address

Mentors and students met in Science and Engineering Library.

2. Meeting Documents

• Agenda for first weekly meeting

• Project Plan

3. Progress Report

We met in person in the Science and Engineering Library. In this first meeting our Mentor

introduced some basic concepts about P&C reinsurance and we discussed the possible

projects. After a discussion, we decided that our project will focus on an analysis of two

types of reinsurance and we plan to build a pricing model from the reinsurance perspective

that will evaluate a XL reinsurance and Quota Share reinsurance for the General Liability

line of business. Some useful reading material is also given by our mentor for next following

weeks.

42

4. Meeting Details

4.1 Explanation of Concepts In Reinsurance

Our mentor explained two different types of reinsurance: Quota share reinsurance and

excess loss reinsurance. For a general liability business, we are planning on considering

a pricing model that will take in to consideration different structures that will be useful

in negotiations with the insurance companies.

4.2 General Idea of Project

Due to different characters shown in liability, such as loss ratio, we can set up a model

and decide which type of reinsurance we should apply. To develop this, we need to

look at historical record of book of business, determine what type of reinsurance

structure we want to play with and project forward to get the fully developed loss,

seeing how it goes under different type of reinsurance. Development triangle is require

to realize this process. After collection and development of date, we can get a fitting

distribution and their statistical character such as volatility, correlation and tail to

decide whether it is a profitable scenario by simulation using software. Our project’s

name could be “General liability reinsurance model”.

4.3 Supplement Comment

There are some features for quota share and excess of loss which are interesting.

For quota share, ceding commission which is the fee reinsurance company need

to pay to insurance for written expense need to be consider carefully cause

there are always credit can be applied when disagreement happen. For excess of

loss, there is a feature called risk statements, which is the cap of loss.

Risk attaching and loss occurring are two types of trending, one is related date

when policies are written and the other one is related to when loss occurs.

There are two ways based on casualty pricing, one is based on experience

which depend on annual book of business, the other on is based on exposure

which is about individual risk.

4.4 Material Recommendation

Basic of reinsurance pricing is a very good article which introduce ways to price

for property and casualty separately.

Presentation in CAS Website

43

4.3 Question:

Citlalli Blanchet: What kind of data we need to get different scenario?

Mentor: In terms of quota share reinsurance, we only need annual premium, expense

and other general data from book of business but in terms of excess

Jiawen Wu: Do we need to test our model?

Mentor: I don’t think we need to worry that part. We can just assume the data are

correct. I rather you focus on concept and modeling building.

5. Date and Time of the Next Meeting

The students and mentors will meet on conference call on Tuesdays.

6. Close

Students prepare for the project plan and send it to mentors.

2/6/2016

Recorded by

Zijun Chen

44


Held on Thursday, 10 June

2016

16:45 pm on Skype

Name Absent



Jiawen Wu

Zijun Chen


Skype call at 4:45 Friday, June 10, 2016


• Agenda for second weekly meeting

3. Progress Report

We had Skype call with mentor for further discussion about our project outline. During

meeting, Mr Kapadia sketched the whole project would be and all steps we are going to

take, which gave us an outline for the whole process. After this, he talked about certain

details in terms of our enquiry, which cleared our confusion on the material given last

week.

45

4. Meeting Details

4.1 Description of Data

Mentor would give us the data with premium, loss, expense and individual claims

which we can analysis individual basis for loss policy, exposure rating, policy limits

something like that. In terms of data, it will be consistent that premium, loss and large

losses all go together.

4.2 Sketch for Whole Project

For quota share, we only do experience analysis but for excess of loss, we do both

experience rating and exposure rating. Firstly, given rate changes, we do group-up

experience anaylsis for projected loss ratio. With alternative loss ratio, we do

experience analysis and exposure analysis and look at different tricky options. After

that, we use simulation, determine distribution and compare different structure.

In terms of quota share, based on projected loss ratio and alternative loss ratio, we can

decide the ceding commission and some adjustment for that. In terms of excess of loss,

for different layer, we calculate exposure loss cost and compare it with experience loss

cost. Based on these two loss cost, we can fit distributions based on them and compare

their statistics feature. After comparison, we can make decision on it.


Assumption is important for this project. We need to list all the assumptions to

from chain ladder to why we switch from experience analysis to exposure

analysis.

Sensitivity test is needed to see how the number changes when assumption

twisted.

46

4.3 Question:

Jiawen Wu: Catastrophe for local enterprise will have huge impact but for

international will be small. So which type are we going to have?

Mentor: We only consider general liability. So the catastrophe impact will be

minimum since they only affect property which is third-party coverage.

Citlalli Blanchet: How do we know whether the exposure analysis or experience

analysis to choose?

Mentor: We need to look at the assumptions. For experience analysis, the company

should be stable, which means no much changes within a long period. For those

companies who raised their policy limits, shifted their area, exposure analysis would be

more suitable.

Zijun Chen: Could you explain more about exposure rating?

Mentor: Exposure rating only depends on in-force exposure. Loss costs are only

calculated by increasing factor, which is nothing to do with historical loss as well.

47


The students and mentors will have a conference call on Thursday morning.

6. Close

Students prepare for the statement of intention and send it to mentors.

10/6/2016

Recorded by

Zijun Chen

48



2016

12:30 pm on Conference

Call

Name Absent



Jiawen Wu

Zijun Chen


Condrence call at 10:00, July 8, 2016


Agenda for second weekly meeting

Worlsheet for ceding commission

Presentation for mid-term

3. Progress Report

We are meeting by a conference call with mentor, he gave us a few advices for our

presentation draft for mid-term have corrected the ceding commission calculation last

week. Next week we are going to have mid-term presentation.

49

4. Meeting Details

4.1 Advice for Mid-Term Presentation Draft

Mr Kapadia suggested us to change our title as reinsurance pricing rather than pricing

quota share and excess of loss reinsurance to avoid too much unnecessary details. he

thought we should give the conception of reinsurance at the beginning rather than in

front of quota share pricing methodology. He give us an example outline for our

presentation: conception of quota share and excess of loss, objective of pricing,

factors we taking into consideration, project basis, summary to show result for quota

share then the methodology used. In terms of excess of loss, we don’t need to go into

details since we haven’t touched yet.

4.2 Correction of Ceding Commission calculation

4.2.1 Sliding Scale

Frist of all, Jiawen explained how we got the ceding commission by sliding scale

commission, profit commission and loss corridor respectively. Then Mr Kapadia

give his option for each method. For sliding scale commission, we only use one

sliding between the commission we want to pay as a reinsurer (minimum) and the

fee the reinsured want to receive (maximum). We decide to use 30%-40% as bound.

For sliding rate, 1:1 is assumed. We don’t need to consider ultimate profit at first but

sliding is needed at the beginning. For convenience, we need to use have 1000

simulation for loss ratio and ceding commission calculated by each method so that

we can see the changes of ceding commission when loss ratio distribution changed.

We don’t need to consider expense and brokerage for sliding scale commission. We

can use middle point of bounds to check our result because the final expected ceding

commission should be nearly there.

4.2.2 Profit Commission

In terms of profit commission, brokerage which is the agency fee for broker between

reinsurance company and insurance company (for quota share, we assume 2% and for

excess of loss, we assume 10%) and margin (we can chose between 10%-15%) is

needed which is the expense for reinsurance company. The ceding commission

reinsurance company want to pay, loss ratio distribution, flat commission and margin

should be decided at the beginning. After we decide the percent return, the final

commission is the sum of flat commission and percent return. Low ceding

commission can be chosen as 30%. If the actual profit is negative, not profit returned

needed. 50% percent return is suggested.

50

4.3 Loss Corridor

Our loss corridor is fine so we don’t need to change it.


Mr Kapadia might come for mid-term presentation next week on Wednesday.

08/07/2016

Recorded by

Zijun Chen

51


Held by Call, 24 June 2016

10:00 a.m.

Name Absent



Jiawen Wu

Zijun Chen


Call conference at 10:00 A.M Friday, June 24, 2016


• Agenda for fifth weekly meeting

• Excel file for triangle calculation

• Experience pricing ppt

• Exposure rating ppt

3. Progress Report

We had a call conference with mentor for fifth discussion about our project. During

meeting, Mr. Kapadia sketched the whole triangle calculation method and some

detailed knowledge about the trend in the calculation, which gave us an outline for the

whole triangle loss calculation. After this, he talked about some concept about the

experience pricing and exposure rating, which cleared our confusion on the material

given last week.

52

4. Meeting Details

4.1 Review of the project charter In the last week, we have uploaded our project charter and sent it to Mr.Kapadia. After

reviewing the whole project charter, he gives us some feedbacks, which indicating that

there are some minor mistakes and he will send an email about the suggestion of the

project charter in the next week.

4.2 Explanation for the triangle calculation

For quota share, we only do experience analysis but for excess of loss, we do both experience rating and exposure rating. Firstly, given rate changes, we do group-up

experience analysis for projected loss ratio. With alternative loss ratio, we do



When we calculate the loss ratio, we need to use the triangle method. Here are some

steps for this method:

Step1–Compile claims data in a development triangle

Step2–Calculate age-to-age factors Step3–Calculate averages of the age-to-age factors

Step4–Select claim development factors Step5–

Select tail factor

Step6–Calculate cumulative claim development factors Step7–Project ultimate claims


• Assumption is important for this calculation. We need to look at the industrial statistics

and assume some inflation rate for our calculation.

53

4.3 Question:

Zijun Chen: There are some age-to-age factors smaller than 1. When we take the

average of these factors, how to deal with those values?

Mentor: We take average of all the values. If the final outcome is larger than 1, we just

keep it, otherwise, we use 1.

Zijun Chen: When we do the triangle calculation, the loss ratio is too large, it seems

something goes wrong.

Mentor: When we check the excel file, there is a mistake in the vba code. After fixing

the code, this problem should be solved.

Zijun Chen: The trends used on premium and loss haven't been decided.

Mentor: We assume the loss trend is 4% , and we need to adjust the project loss.s

54


The students and mentors will have a conference call or in-person meeting on next

Thursday.

6. Close

Students prepare to complete the triangle calculation and send it to mentors.

25/6/2016

Recorded by

Jiawen Wu

55


Held on Thursday, June 30th 2016.

Phone call.

Name Absent


TA Ehtesham Malik Student Citlalli Blanchet

Jiawen Wu

Zijun Chen


Mentors and students met in a conference call.


• Agenda for meeting.

• Project Charter.

• Loss Gross triangles.

3. Progress Report

We discussed the comments that Mr. Kapadia had on the Project Charter. We talk

about the approach that we were going take in our midterm presentation. We also talk

about some modifications that we need to add the gross loss triangle calculations.

Finally, we discuss the simulation process and the use of the @Risk software.

56

4. Meeting Details

4.1 Comments on Project Charter

We currently have the project in three phases: 1.- Data analysis 2.- Loss cost analysis.

3.-Pricing analysis.

Mr, Kapadia suggested to have the phases more like 1.-Data analysis and projecting

Ground up losses. 2.- Pricing of Excess of Loss and Quota Share reinsurance. 3.-.

Final decisions and over all summary result analysis.

We agreed that we will decide on the best split of the phases in the future but this

could be the approach that we should be taking.

4.2 Midterm presentation discussion.

The midterm presentation is due in two weeks, we talk about the approach that we

should take and what topics should we mention in more detail.

Mr. Kapadia suggested presenting an overview of the project by giving an introduction

to reinsurance, explaining what General Liability is and defining the types of

reinsurance that we are planning to price. Then give definitions and examples of

Excess of Loss and Quota share insurance and comment on the assumptions. Since for

the Quota Share reinsurance we have already been working the Gross Loss triangle we

can explain a little more in detail our results and calculations. Then we can give an

introduction to the treaty features that we are applying and their definitions. For the

Excess of loss insurance we can give an introduction of the pricing plan and talk about

the data available for this analysis. We can also show a list of assumptions that we so

far have used and the one we will need to consider. In general to give a non to technical

presentation of our project but that at the same time will give a clear overview of our

progress and our objectives.

4.3 Discussion on Gross Loss Triangle calculations.

We suggested to add different averages and methods of obtaining the Loss

Development Factors because in our data we have some years with salvage and

subrogation. We agreed to add these calculations and discuss our finding in our next

meeting.

4.4 Discussion on Simulation on Loss Ratios.

57

We agreed that the software @Risk is our best option to work with simulations and

tests of distributions that best fit our data.

We agreed that we all are going to come up with some data analysis and discuss our

finding in our next meeting. We all need to get more familiarized to @Risk. We all

are very interested in learning how to use it since is a software that is commonly

used in the reinsurance industry.

We discussed options on how to come out with our results. Like what happens if we

add some catastrophic losses. Try different approaches in terms of tests and

simulations. 4.5 Discussion about commissions.

We discussed how to add a sliding scale commission. And then how to get our profit

and what can be a reasonable profit commission all based on the simulations of the

Loss Ratios. And we want to calculate the expected value of this commission.

We also wanted to discuss reasonable profit limits.

Mr. Kapadia suggested to add a table with the expected losses and the different

commission that we will consider.

Bibliography



Presentation in CAS Website.


The students and mentors will meet on conference call which hasn’t be decided.

6. Close

Students prepare an outline of the midterm presentation. And we will discuss the

simulation analysis

6/30/2016

Recorded by

Citlalli Blanchet

58


Held on Thursday, 4 July 2016

17:00 pm in Person

Name Absent



Jiawen Wu

Zijun Chen


In person meeting at 5:00 Thursday, July 4, 2016


• Agenda for 11th weekly meeting

3. Progress Report

We had in person meeting with mentor for further discussion about our exposure

rating. During meeting, Mr. Kapadia explain how we get loss ratio for each layer

for exposure rating using ILFs. After this, he talked about how we are going to

make final decision between quota share and excess of loss. He also suggested us

an outline for final presentation.

59

4. Meeting Details

4.1 Description of Data

We have details about information of individual policy from ceding company,

including policy limit, premium, effective date and etc., which affect loss of

reinsurance company directly. ILFs are also given for each layer’s base premium.

4.2 Sketch for Whole Project

In order to get loss ratio for 4M/1M and 3M/2M reinsurance policy, we need to

calculate adjusted premium for each layer separately. We can get base premium

by dividing ILFs from premium and multiple the difference between upper limits

and lower limits, which is decide by both layer and policy limit, we get premium

for each layer. We assume each layer has loss ratio 55%. By applying this loss

ratio, we get expected loss for each layer. Percentage of premium compared with

totally premium multiple corresponding expected ratio is the total expected loss

for each layer. We sum them up then we get the ultimate loss for 4M/1M and

3M/2M layer individually.

Since we have loss ratio from both exposure rating and experience rating, we

weigh two values and come up a credible loss ratio for excess of loss based of in-

force policy and historical policy. In order to compare quota, share and excess of

loss, we need to consider qualitatively as well beside volatility, profit margin and

other consideration. We are going to have a table containing quota share, excess

of loss with 4M/1M layer and 3M/2M layer, including premium ceded, loss

cause, expense ceded, brokerage fee and profit margin (we require 10% as

reinsurer)


No meeting afterwards but we will keep contact with Mr Kapadia by email.

6. Close

Finish final calculation about exposure rating.

06/08/2016

Recorded by

Zijun Chen

60



2016

12:30 pm on Conference

Call

Name Absent



Jiawen Wu

Zijun Chen


Condrence call at 12:30 Thursday, June 16, 2016


Agenda for second weekly meeting

Project Charter

3. Progress Report

We are meeting by a conference call with mentor, he explained the data he provided

us and explain the work we need to do with our data also how to use the result in

further plan. Assumptions and adjustment examples are given in the call as well

61

4. Meeting Details

4.1 Explanation of Data

Mentor cleared our confusion with the data provided and deleted all the useless data

from table. The important data we are going to use are effective data, expiration date,

loss and expense and limit. We can ignore status since no matter what status the

claims have, they have potential.

We have three sheet so far. Policy listing are all losses while individual loss only

includes losses above $500k. The triangle sheet is for us to get the loss ratio. In terms

of individual loss, we are going to get increasing limit factors by seeing the changes

of premium based on different layers of limit so that we can use exposure rating. For

whole loss, we are using experience rating.

4.2 A Few of Steps on Data

First step is getting loss ratio based on triangle sheet. After that is working on large

loss which we are going to build in trend to loss by seeing how much historical loss

in these layers. Large loss won’t be used in quota share but only for excess of losses.

4.2 Tech in Data Analysis

Ultimate loss, loss development for triangle and exposure rating, experience rating

for reinsurance pricing will be used.

4.3 Assumption

Trend for premium, ceding commission, expense, rate changes for bringing the

premium on level. We need to give more weight on recent year if there are any

trend showing in the data.

4.3 Question

Q: where are we going to use the simulation?

62

A: We will use simulation after we decide the loss ratio for quota share and loss

cost for excess of losses. We will depend on the distribution but not point. Ceding

commission depends on the probability based on distribution. While we may don’t

have tail in our data. 5. Date and Time of the Next Meeting

The students and mentors will probably have a meeting in person on Next Thursday.

6. Close

Students prepare for the Project Chapter and send it to mentors.

16/6/2016

Recorded by

Zijun Chen

63


Held by Call, 20 July 2016

12:30 a.m.

Name Absent



Jiawen Wu

Zijun Chen


Call conference at 12:30 A.M Friday, July 20, 2016


• Agenda for weekly meeting

• Experience pricing

3. Progress Report

We had a call conference with mentor for discussion about our project. During

meeting, Mr. Kapadia sketched the whole experience rating and some detailed

knowledge about the trend in the calculation, which gave us an outline for the whole

experience rating calculation. After this, he talked about some concept about the

experience pricing and exposure rating, which cleared our confusion on the material

given last week

64

4. Meeting Details

4.1 Review of the project charter In the last week, we have uploaded our midterm presentation and sent it to Mr.Kapadia.

After reviewing the whole midterm presentation, he gives us some feedbacks, which

indicating that there are some minor mistakes.

4.2 Explanation for the experience rating calculation






Data Needed:

- Historical WP or EP - Historical Rate Changes

- Projected Rate Change - Loss and exposure trend

- Individual losses / claims listing - Excess loss development factors (usu. Derived if not available)





The students and mentors will have a conference call or in-person meeting on next

week.

6. Close

Students prepare to complete the triangle calculation and send it to mentors.

23/7/201

Recorded

by Jiawen

Wu

65

Minutes of the Eight Group Meeting of Integrated Project

Held on Thursday, July 28th 2016.

Phone call.

Name Absent


TA Ehtesham Malik Student Citlalli Blanchet

Jiawen Wu

Zijun Chen


Mentors and students met in a conference call.


• Agenda for meeting.

• Experience rating calculations.

3. Progress Report

We discussed the final presentations dates and details about the Experience rating and

the Exposure rating calculations for the Excess of loss reinsurance. Finally, we

discussed our plan to manage our time from now to the date of the final

presentation.

4. Meeting Details

4.1 Discussion about final presentation.

In our meeting with Professor Noor we found out that we will need to finish our

project and the final presentation one week before of the previously planned date. Our

mentor will be out of town for the last two weeks of the project with no internet access,

so we needed to discuss our progresses and the expected dates of each step in order to

meet the deadlines. We agreed on meeting next Thursday in person. In this meeting

we are planning to have a better understanding of the last steps and conclusions as well

as an outline of the final presentation.

66

4.2 Experience rating calculations.

By the time of our meeting we finished our experience rating calculations. We sent our

file to our mentor. We had questions about the how to calculate the losses in each layer

of the Excess of loss reinsurance. We are considering two layers, 3M xs 2M and 4M xs

1M. We agreed that we need first to trend the individual losses and then separate the

losses corresponding to our layers. The trend calculations for each loss will be from

January of each accident year to July 1st of Ay 2016. After trending the losses we

aggregated them by accident year and then we applied the Loss development factors

calculated previously in our Gross Loss triangles used in the Quota Share calculation.

Then we applied the Chain Ladder and B-F method to obtain the Ultimate developed

losses. We used the on level premium also calculated previously in the Quota Share

analysis to obtained the Experience Loss cost,

4.3 Discussion on Exposure rating.

We discussed the theory involved in the Exposure rating and we concluded that it

would be easier to understand it if we see an example that Mr. Kapadia will share with

us and also discuss it in our in person meeting next week.

4.4 Discussion on in person meeting.

We agreed to try to meet at the Lamont campus next week. This will be our last

meeting with our mentor before the final presentation.

Bibliography



Presentation in CAS Website


The students and mentors will in person next week time and place to be determined.

6. Close Students prepare an outline on Experience rating and come up with questions for our in

person meeting.

7/28/2016

Recorded by

Citlalli Blanchet

67


Held by Call, 11 Aug 2016

12:30 a.m.

Name Absent



Jiawen Wu

Zijun Chen


Skype conference at 6:30 P.M Thursday, Aug 11, 2016


• Agenda for weekly meeting

• Exposure pricing

• Final Presentation

3. Progress Report

We had a Skype conference with our teammates for discussion about our project.

During meeting, our members sketched the whole exposure rating and some detailed

knowledge about the final presentation, which gave us an outline for the whole

reinsurance pricing calculation. After this, we talked about some concept about the

final comparison chart between quota share and excess of loss, which cleared our

confusion on the material given last week.

68

4. Meeting Details

4.1 Review of the project charter In the last week, we have discussed our exposure rating and sent it to Mr.Kapadia.

After reviewing the whole calculation, he gives us some feedbacks, which indicating

that there are some minor mistakes.

4.2 Explanation for the exposure rating calculation






Data Needed:

- In-force policy listing or In-force limit profile

- Increased Limit Factors (ILFs)

- Projected Ultimate Ground-up Loss Ratio

Steps:

- Determine portion of premium for excess layer using ILFs

- Calculate expected loss using ground-up loss ratio

- Aggregate across all policies or limits

And then we talked about the final comparison between excess of loss and quota share.

And give a comparison chart for our final presentation.





It will be the final presentation.

6. Close

Students prepare to complete the final presentation and final report and send it to

mentors.

23/7/2016

Recorded by

Jiawen Wu

69

Date: 06/10/2016

Time: 5:00 PM

Timekeeper: Jiawen Wu

7.4 Agenda

MEETING AGENDA – Group 5 P&C

[Second GROUP MEETING OF INTEGRATED PROJECT]

MEETING INFORMATION

Objective: Work on the outline of the phase of the project for the Statement of Intent.

Meeting moderator: Citlalli Blanchet

Meeting Type: Skype Meeting

Note Taker: Zijun Chen

Attendees: Sandip Kapadia, Jiawen Wu, Zijun Chen, Citlalli Blanchet

PREPARATION FOR MEETING

Please Read: Reinsurance Pricing: Practical Issues & Considerations.

ACTION ITEMS FROM PREVIOUS MEETING

-- Review literature for Reinsurance pricing.

AGENDA ITEMS

ITEM PRESENTATER APPROX. TIME (MIN)

1. Discuss in more detail phases of the analysis. All Atte ndees 30 mins

2. Outline of Statement of Intent. All Attendees 20 mins

3. Net meeting appointment and expected deliverables. All Attendees 10 mins

70

OTHER NOTES OR INFORMATION

Question List:

1. Especifications expected in the data.

2. Which kind of extreme events can we expect?

3. Explanation of Exposure rating.

71

Date: 06/16/2016

Time: 12:30 AM

Timekeeper: Zijun Chen

MEETING AGENDA –

[SEVENTH GROUP MEETING OF INTEGRATED PROJECT]

MEETING INFORMATION

Objective: Start data analysis and model building

Attendees: Zijun Chen, Citlalli Blanchet


Please Bring: Project Charter


Meeting Type: Conference call

Note Taker: Jiawen Wu

-- Review the book of business data and start analysis

AGENDA ITEMS

1. Progress Report


- Reference reading All Attendees 10 mins.

- Introduction of this week’s working

2. Data Analysis Discussion

- Discuss steps for data analysis

- Find out features and limits for out data All Attendees 60 mins.

3. Question and Ask

- Questions All Attendees 40 mins.

4. Next Meeting appointment All Attendess 5 mins.

72

MEETING AGENDA –


MEETING INFORMATION

Objective: Discuss the possible projects and come up with a first draft for the Project plan.

Date: 06/02/2016

Time: 12:00 PM Meeting Type: In-person Meeting

Timekeeper: Jiawen Wu Note Taker: Zijun Chen

Attendees: Sandip Kapadia, Jiawen Wu, Zijun Chen, and Citlalli Blanchet

AGENDA ITEMS


1. Introduction

All attendees 20 mins

2. Discussion of possible project Sandip Kapadia 20 mins

3. First Draft of Project plan All attendees 20 mins

73


[GROUP MEETING OF INTEGRATED PROJECT]

MEETING INFORMATION

Objective: Work on the corrections of the Project Charter. Discuss project time line and Experience rating and Exposure rating techniques.

Date: 06/23/2016

Time: To be determined

Meeting Type: Skype Meeting

Timekeeper: TJiawen Wu Note Taker: Zijun Chen


Attendees: Sandip Kapadia, Jiawen Wu, Zijun Chen, Citlalli Blanchet



De-Mystifying Reinsurance Pricing.


-- Discusses Project Charter and time line of project.

AGENDA ITEMS


1. Discuss Project Charter commentaries and corrections. All Attendees 20 mins

2. Discuss time line of project All Attendees 20 mins

3. Discuss loss triangles and Experience and Exposure

rating methods All Attendees 20 mins

74



MEETING INFORMATION

Objective: Work on the corrections of the Project Charter. Determine the ceding commission of quota share method. Discuss about the simulations for excess of loss.

Date: 06/30/2016

Time: Noon Meeting Type: Call

Timekeeper: Jiawen W u Note Taker: Zijun Chen


Attendees: Sandip Kapadia, Jiawen W u, Zijun Chen, Citlalli Blanchet






AGENDA ITEMS



2. Determine the ceding commission of quota share

method

All Attendees 20 mins

3. Discuss about the simulations for excess of loss.


75



MEETING INFORMATION


Date: 06/30/2016










AGENDA ITEMS



2. Determine the ceding commission of quota share

method


3. Discuss about the simulations for excess of loss.


76

MEETING AGENDA –


MEETING INFORMATION

Objective: Introduction of excess of loss

Date:

Time: Meeting Type:

Timekeeper: Zijun Chen Note Taker: Jiawen Wu

Attendees: Zijun Chen, Citlalli Blanchet


Please Bring: Agenda, reading material


-- Understanding steps of excess of loss rating

AGENDA ITEMS

1. Progress Report


- Reference reading All Attendees 10 mins.

- Introduction of this week’s working

2. Going through excess of losing pricing

- experience rating

- exposure rating All Attendees 60 mins.

3. Question and Ask

- Questions All Attendees 40 mins.

4. Next Meeting appointment All Attendees 5 mins.

77



MEETING INFORMATION


Date: 07/28/2016










AGENDA ITEMS

ITEM PRESENTATER APPROX. TIME (MIN) 1. Discuss experience rating and corrections. All Attendees 20 mins

2. Determine the loss ratio of experience rating method All Attendees 20 mins

3. Discuss about the exposure rating.


78

Date: 07/07/2016

Time: To be determi




MEETING INFORMATION

Objective: Review the midterm presentation. Discuss simulations of Loss Ratio and ceding commission calculations.

ned Meeting Type: Conference call



Attendees: Sandip Kapadia, Jiawen Wu, Zijun Chen, Citlalli Blanchet.


Please Read: Midterm Presentation.


-- Ceding commissions discussions.

AGENDA ITEMS

ITEM PRESENTATER APPROX. TIME (MIN) 1. Discuss Midterm presentation All Attendees 20 mins

2. Discuss Loss ratio distribution fit and simulations All Attendees 20 mins

3.

Discuss Ceding commission calculations.

All Attendees

20 mins

79



MEETING INFORMATION


Date: 08/11/2016

Time: Noon Meeting Type: Skype








-- Discusses Final Presentation and exposure rating.

AGENDA ITEMS


1. Discuss exposure rating. All Attendees 20 mins

2. Determine the final comparison chart for quota share

and excess of loss


3. Discuss the final presentation.


1

Date: 04/08/2016

Time: After 5pm


MEETING AGENDA –


MEETING INFORMATION

Objective: Final decision between quota share and excess of loss

Meeting Type: In person


Attendees: Zijun Chen, Citlalli Blanchet, Jiawen Wu


Please Bring: Agenda, worksheet for exposure rating


-- Calculate expected loss for exposure rating

AGENDA ITEMS


1. Check the result of exposure rating

- Compare two worksheets All Attendees 20 mins.

- Correction

2. Make final determination between Quota Share and Excess of Loss

- Criteria for final decision

- Steps and tools to realize the calculation All Attendees 30 mins.

3. Presentation

- Suggestion to presentation outline All Attendees 10 mins.

4. Next Meeting appointment All Attendees 5 mins.