Actuarial Challenge 2015 Price Indemnity Puzzle Contest Insurance Report

Prize Indemnity Insurance Puzzle Promotion Insurance

01-Feb-15

Actuarial Challenge Insurance Ltd.

Author:

Ahmad Ashraf Zafrullah

Ain Nadhirah Muhammad

Fatin Umirah Faridon

Muhammad „Afif Amir Husin

Muhammad Hazrani Abd Halim

Muhammad Fauzan Rusli

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EXECUTIVE SUMMARY

This project have an objective; developing and pricing a premium for Puzzle Promotion Insurance.

The insurance product is to cover the prize that promote by IT Mall (Y2K Mall). IT Mall will not

retain any amount of prize that they offer. Therefore, all claims will be made through Actuarial

Challenge Insurance Limited (ACI).

There are two information that IT Mall provided us. First, the format of the competition. It consists

of 5 stages, which all stages need to be completed by the participants and have different number of

puzzles that the participant need to solve. There are specific formula to measure Total Time Used

(TTU) by each participants. Second, we are given time to completion for each puzzle. This puzzle

game have been played by professional computer gamers to test the difficulties of the aforesaid

computer puzzles.

By using both information, we will find the premium that affordable for the company.

Four specific methods is used in this project. First method we use is drawing histogram to determine

the distribution. Second, we use Monte Carlo technique for simulation. Then, premium is calculated

considering expenses and profit charges. Next, Inverse Transform Method is used to find time

premium for 90th, 99th, and 99.5th percentile.

Based on the result, pure premium price is RM 16,370 while quoted premium is RM 27,283.30. After

decreasing time of completion to 5%, profit obtained by our company will be 9.5% and after

decreasing by 10% is profit at 0.1%.

Keywords: Monte Carlo, Inverse Transform, Pure Premium and Quoted Premium

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TABLE OF CONTENTS EXECUTIVE SUMMARY ........................................................................................................................ 2

INTRODUCTION ....................................................................................................................................... 4

1.1. Background of Company .................................................................................................................. 4

1.2. Prize Indemnity Product.................................................................................................................... 4

1.3. Potential benefits of insurance: ......................................................................................................... 4

1.4. Insurance costs: ................................................................................................................................. 5

PUZZLE PROMOTION INSURANCE ................................................................................................... 6

2.1. Introduction of product ..................................................................................................................... 6

2.2. Target Market .................................................................................................................................... 6

2.3. Potential Risk .................................................................................................................................... 6

2.4. Disclosure ......................................................................................................................................... 6

2.5. Coverage ........................................................................................................................................... 7

2.6. Exclusion........................................................................................................................................... 7

2.7. Claim ................................................................................................................................................. 7

2.8. Termination ....................................................................................................................................... 7

METHODOLOGY ..................................................................................................................................... 8

3.1. Premium Pricing ............................................................................................................................... 8

3.2. Profit Testing .................................................................................................................................. 12

RESULT & DISCUSSION ....................................................................................................................... 13

4.1. Premium Pricing ............................................................................................................................. 13

4.2. Profit Testing .................................................................................................................................. 14

CONCLUSION ......................................................................................................................................... 15

APPENDIX ................................................................................................................................................ 16

SHEET 1 ..................................................................................................................................................... 16

SHEET 2 ..................................................................................................................................................... 16

VBA CODING............................................................................................................................................ 17

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INTRODUCTION

1.1. Background of Company

Actuarial Challenge Insurance Limited (ACI) is a globally renowned specialist insurance provider

specializing in personal and commercial insurance offerings. ACI gets to know their clients based on the

details the clients are willing to share so then ACI can offer target insurance coverages that fit their

specific needs. ACI is dedicated to creating strong relationships with its customers, insurance carriers, and

employees. As an independent agent, ACI can collaborate with the best insurance carriers and provide

more than one option. ACI can tailor a program to fit client‟s needs by placing them with one insurance

carrier that covers all their needs, or place coverage with separate carriers. It is all about options.

1.2. Prize Indemnity Product

Prize Indemnity Insurance allows an event organizer or sponsor to offer a risk-free large prize at a

fraction of the prize value. It can be used as a way to attract a crowd, create a buzz, and make the event

exciting and unique.

An insured promotion enables the promoter or sponsor to accurately budget for the cost of the prize and

protect the company‟s balance sheet from any unnecessary liability.

Over the last few years, the demand for prize indemnity insurance has increase due to the growing

popularity of promotions and contests. Companies are recognizing that hosting a contest is allowing them

to gain more exposure to their consumer base as opposed to traditional advertisements and sponsorship

events. Americans are regularly reminded about promotions and their prizes through newspapers, state

lotteries, and scratch ‟n‟ win games. With all these chances to win, prizes are increasing in monetary

value to remain competitive over other promotions, and to keep up with the demand of the American

culture of chance. If prizes are becoming more valuable, the need for prize indemnity insurance becomes

more important.

1.3. Potential benefits of insurance:

i. Create buzz

ii. Generate brand awareness

iii. Draw customer attention

iv. Expand customer or client list

v. Boost sales and demand

vi. Create a viral market

vii. Low to no risk on the part of the promotion

host

1.4. Insurance costs:

Insurance costs and premiums vary on the promotion being considered and the potential risk for

customers to win. When developing a quote for a client, past promotions and the level of difficulty of the

promotion are taken into consideration.

Three main factors that determine the cost of prize insurance include:

1. Level of difficulty of the promotion

2. Number of attempts to win prize

3. Actual retail price of prize to be awarded

The more difficult the promotion, the fewer attempts that are made to win the prize, and the lower the

value of the prize the less expensive the prize indemnity insurance will cost.

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PUZZLE PROMOTION INSURANCE

2.1. Introduction of product

Promotion Insurance is just one popular type of insurance plan offered by insurance providers. The

origins of promotion insurance date back to the early 1980s with golf tournaments. Puzzle game hosts or

sponsors purchase puzzle promotion insurance in order to cover the costs of awarding participants the

prize for successfully solving all puzzle provided during the day. The best part about puzzle promotion

insurance is its flexibility. It can be tailored based on the price that the host required. This type of

insurance allows more than one participant to win the prize being offered.

2.2. Target Market

This insurance is tailored specifically for the organizer of puzzle competition hosts. It may come from

various companies that want to promote their companies and sponsors.

2.3. Potential Risk

1. Over insurance: unattractive/unaffordable premium price for Y2k Mall.

2. Under insurance: under-valued premium price may jeopardize ACI‟s future profit target, or

experience huge loss.

3. Sensitive insurance terms: any changes of circumstance of Y2k Mall‟s computer puzzle

contest, will require Y2k Mall to quickly notify ACI.

4. Documentation error: Any slight error of information documented may result in rejection of

claims.

5. Moral Hazard: There are a few possible cheating methods identified that can be used by the

computer puzzle contest participants.

2.4. Disclosure

The name and identification card

Proof of expenditure (with minimum amount of RM2000.00) is required in the form of a receipt dated

during the contest period.

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2.5. Coverage

The insurer will indemnify RM10,000 for each participants who can attain that the total time used for

solving the puzzle less than 20 minutes and total number of puzzles not more than 25. This insurance is

only covered for the contest day.

2.6. Exclusion

No coverage shall apply where:

a. There are more than 100 participants.

b. Multiple entries for each participant

c. The participant winning the insured contest is employees, agents, advertising agencies and direct

suppliers (including their immediate family members) of Y2k Mall

d. Any contravention of the Terms or Conditions of the policy or violation of the Contest Regulations

occurs.

e. Fraud, Misrepresentations, Dishonesty or Collusion occurs.

2.7. Claim

Any claim made under this policy must be substantiated by providing all pertinent information required.

ACI is not responsible for any monetary charges brought forth by obtaining the claim information needed

by Y2k Mall. Any incomplete documentation will be returned to you for completion.

2.8. Termination

This policy may be cancelled by Y2k Mall prior to the Y2k Mall Tournament by submitting written

notice to the Broker and the ACI will return the premium stated in the Declaration page. This policy may

not be cancelled by the Y2k Mall once the Y2k Mall Tournament has commenced.

ACI reserves the right to cancel this policy upon thirty (30) days written notice. In the event of

cancellation, any unused premium will be returned to Y2k Mall.

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METHODOLOGY

3.1. Premium Pricing

Figure 3.1: Flowchart for premium pricing

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The following are the steps to determine the quoted premium bases on Figure 3.1:

1) Determine the distribution of the data give by Y2k Mall. The data is analyze using histogram.

Based on the histogram drawn, the distribution of data is suit with exponential distribution.

Stage 1:

Stage 2:

Stage 3:

Stage 4:

Stage 5:

10

2) To see whether the data fit with exponential distribution, QQ Plot method is used. Based on the test,

the data fit with exponential distribution.

Stage 1:

Stagen 2:

Stage 3:

Stage 4:

Stage 5:

11

3) Calculate average time for every stages. The formula for the average time:

𝑡𝑖 = 𝑛

100

𝑤𝑕𝑒𝑟𝑒;

𝑡 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 𝑒𝑣𝑒𝑟𝑦 𝑠𝑡𝑎𝑔𝑒

𝑖 = 𝑠𝑡𝑎𝑔𝑒 𝑛𝑢𝑚𝑏𝑒𝑟

𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑧𝑧𝑙𝑒𝑠

4) Simulate using Monte Carlo simulation technique for each stages condition according to

exponential distribution.

𝑒 = −𝑚𝑒𝑎𝑛 × log 1 − 𝑝 ; 𝑝 𝑖𝑠 𝑟𝑎𝑛𝑑𝑜𝑚, 0 ≤ 𝑝 ≤ 1

5) Get the state of winning according to two conditions;

TTU is less or equal to than 1200 seconds

Number of puzzles is less or equal to 25

State 1 if win

State 2 if loss

6) Randomly choose 100 outcomes from randomly generated 1000. Number of winners is recorded

among the 100 shoppers. This step is simulated for 1000 times to obtain the expected payment

amount

7) Calculate Pure Premium using formula:

𝑃𝑢𝑟𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑖𝑐𝑒 𝑎𝑚𝑜𝑢𝑛𝑡

8) Calculate the premium using formula:

𝑄𝑢𝑜𝑡𝑒𝑑 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑃𝑢𝑟𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 × 1

0.6

9) Charge expenses on quoted premium using formula,

𝐸𝑥𝑝𝑒𝑛𝑠𝑒 = 𝑄𝑢𝑜𝑡𝑒𝑑 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 × 0.15

Increase the q

𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑄𝑢𝑜𝑡𝑒𝑑 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 × 0.25

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10) Draw histogram and Cumulative Distribution Function (CDF)

11) Calculate the percentile by using interpolation method for 0.9, 0.95 and 0.995.

12) Perform profit testing by decreasing time to solve each puzzle by 5% and 10%.

3.2. Profit Testing

In order to test the profit gain by the company, based on the premium calculated above we try to decrease

time to solve each puzzle by 5% and 10%.

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RESULT & DISCUSSION

4.1. Premium Pricing

1) Expected Prize Money = Pure premium

𝑃𝑢𝑟𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑅𝑀16,370.00

0

50

100

150

200

250

300

350

400

Histogram of simulated Prize

0200400600800

10001200

Cumulative distribution of simulated

prize

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2) Quoted Premium, Q

𝑄 = 𝑃𝑢𝑟𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 + 0.15𝑄 + 0.25𝑄

𝑄 = 𝑅𝑀27,283.30

3) Total Prize at 90th percentiles = RM25, 744.40

4) Total Prize at 95th percentiles = RM33, 085.10

5) Total Prize at 99.5th percentiles = RM50, 377.80

4.2. Profit Testing

Profit Test: data point decrease to 5%

i. Pure Premium = 𝑅𝑀20,610.00

ii. Quoted Premium, Q

𝑄 = 𝑃𝑢𝑟𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 + 0.15𝑄 + 𝑃𝑟𝑜𝑓𝑖𝑡 ∗ 𝑄

𝑃𝑟𝑜𝑓𝑖𝑡 = [email protected]%

Comment:

By decreasing all data points in “Task_1_data.xls” by 5%, we found that the expected

profit is reduced. However, we can still obtain profit of 9.5% of the Quoted Premium.

Profit Test: data point decrease to 10%

i. Pure Premium = RM23,140.00

ii. Quoted Premium, Q

𝑄 = 𝑃𝑢𝑟𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 + 0.15𝑄 + 𝑃𝑟𝑜𝑓𝑖𝑡 ∗ 𝑄

𝑃𝑟𝑜𝑓𝑖𝑡 = [email protected]%

Comment:

By decreasing all data points in “Task_1_data.xls” by 10%, we found that the expected

profit is reduced. However, we can still obtain profit of 0.19% of the Quoted Premium but

the profit is very low. It is not worth to produce the product.

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CONCLUSION

It is concluded that the quoted premium is RM 27,283.30. The quoted premium is found by using three

specific techniques. Techniques that used in this project are Histogram to find suitable distribution, Monte

Carlo simulation and Inverse Transform method. The quoted premium have considered, number of

winners with 0.17%, 15% expenses and 25% profit charges. After 5% decrement of time completion, the

quoted premium became more expensive, but still profit 9.5% compare to before, 25%. With 10%

decrement, it is not acceptable because the profit gain by the company is only 0.19%.

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APPENDIX

SHEET 1

SHEET 2

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VBA CODING

Sheet1

Option Explicit

Private Sub CommandButton1_Click()

Dim i As Double

Dim k As Integer

Dim n As Long

Dim mean() As Double

ReDimmean(6)

Dim noSimulation As Double

Dim randomize As Double

ReDimmean(6)

Dim epsilon As Double

Dim stage() As Double

Dim level() As Double

With ActiveSheet

Range("AH3:AS1002").Clear

noSimulation = Val(.Cells(5, 8).Value)

ReDimstage(noSimulation, 6)

ReDimlevel(noSimulation, 6)

For k = 1 To 5

mean(k) = Val(.Cells(102, k).Value)

Next

For k = 1 To 5

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For i = 0 To (noSimulation)

epsilon = -mean(k) * Log(1 - Rnd)

stage(i, k) = Fix(epsilon)

Next

Next

'Stage1

For k = 1 To (noSimulation)

For n = 1 To 5

randomize = Fix(noSimulation * Rnd)

level(n, 1) = stage(randomize, 1)

.Cells(2 + k, 10 + n).Value = level(n, 1)

Next

Next

'Stage2


For n = 1 To 4




Next

Next

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'Stage3


For n = 1 To 3




Next

Next

'Stage4


For n = 1 To 2




Next

Next

'Stage5



n = 0

Do Until stage(randomize, 5) < 300 Or n = 11

.Cells(2 + k, 34 + n).Value = stage(randomize, 5)

n = n + 1


Loop

.Cells(2 + k, 34 + n).Value = stage(randomize, 5)

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.Cells(2 + k, 46).Value = n + 1


n = 0

Next

End With

End Sub

Documents

Actuarial Challenge 2015 Price Indemnity Puzzle Contest Insurance Report