Modelling Non-Life Insurance

Modelling Non-Life Insurance

Case study:

Modelling a (virtual) non-life insurance company « Feldafinger Brandkasse»,developed 2006 by German Actuarial Association (DAV) for the needs in education and training

Prof. Dr. Martin Balleer Georg-August-Universität GöttingenGermanyEuropean Actuarial Academy GmbH

Agenda

•Structure of a DFA-model (deterministic and stochastic approach) of a non-life insurance company

•Analysis of a virtual non-life company with two business lines (MTPL, building insurance)

•Modelling techniques and results for claims, reserve risks, asset risk, reinsurance, underwriting risks

Modelling non-life insurance

Corporate planning- A deterministic approach -

Modelling non-life insurance

Corporate planning

Corporate planning

Corporate planning

Corporate planning

number of contracts

Corporate planning

Corporate planning

= costs of the claims managment

Corporate planning

Corporate planning

reserves that are estimated when claims are reported

Corporate planning

Corporate planning

Corporate planning

Corporate planning

Corporate planning

Modelling a company- A stochastic approach -

Modelling non-life insurance

Modelling non-life insurance

Economic result function

= technical cash-flow

Modelling non-life insurance

The distribution functions of claims of a single risk are known. In orderto calculatie the distribution function of the whole portfolio the individual functions have to get aggregated under the assumption that the risks are independent from another.

Modelling non-life insurance

Modelling non-life insurance

Modelling of claims

Modelling non-life insurance

Modelling non-life insurance

Claims modelling

It is useful to cluster claims in•Attritional•Large•CATclaims with regard to modelling

Modelling non-life insurance

Stochastic modelling of claims

Modelling non-life insurance

Modelling of attritional claims (MTPL)-on Ultimate Basis –

Comment: „Ultimate Basis“ means that the final payments of claims are considered

Modelling non-life insurance

Modelling attritional claims (MTPL)

Modelling non-life insuranceModelling attritional claims (MTPL)

Modelling non-life insurance

Separate modelling of claims frequeny and claims severity

Modelling non-life insurance

Modelling of attritional claims frequency (1/3)

Modelling non-life insuranceModelling of attritional claims frequency (2/3)

Modelling non-life insurance

= 64,2 x 378.610

Modelling of attritional claims frequency (3/3)

Modelling non-life insurance

Modelling of attritional claims average (1/2)

Modelling non-life insuranceModelling of attritional claims average (2/2)

Modelling non-life insurance

not presentedin this lecture

= 2820 x 24,3

Result: Modelling of attritional claims incurred in 2006

Modelling large claims (MTPL)

Modelling non-life insuranceModelling large claims

Modelling non-life insuranceModelling large claims

Modelling non-life insurance

over 3 years

Modelling non-life insurance

Modelling non-life insurance

(for 1 mio exposure)

backtesting:3,3 = 8,8 x 0,371

number of claims

= 8,8 x 378

Modelling non-life insuranceModelling of large claims severity

Modelling non-life insurance

= 3,3 x 1,919

Modelling Building/CAT claims

Modelling non-life insurance

Modelling non-life insurance

Modelling non-life insuranceModelling CAT claims

Modelling non-life insurance

Modelling CAT claims

Modelling non-life insurance

Modelling CAT claims

Modelling non-life insurance

DFA model„Feldafinger Brandkasse“

DFA model

DFA model

DFA = Dynamic Financial Analysis

DFA model

DFA model

DFA model

DFA models are rather complex because of many simulations and many LOB and difficult to handle

DFA model

DFA model

following corporateplanning

DFA model

Expected claims (total):

68,5 + 3,3x1,9 18= 74,8

see above

Distribution of severity losses CAT risks

CAT losses

RBC ( = Risk Based Capital) calculationwithin DFA

Comment: RBC stands for the required capital; in Solvency II it is named SCR (Solvency Capital Requirement)

DFA model

DFA ModelRisk aggregationwithin Solvency II

Source: DAV-CERA Modul, Klassifizierung und Modellierung von Risiken

defaultmarket underwriting 1.aggregation

2. aggregation

DFA model

DFA model

RBC = TVAR - Mean

DFA model

DFA model

DFA model

DFA model

(building)

DFA model

DFA model

DFA model

DFA model

Reserving risk

DFA model

DFA model

DFA model

Economic result: + 5,9 Mio €

DFA model

(RBC)

DFA model

Results on Company level

TVaR allocation method

DFA model

(before RI and CoC)

DFA Model

Return =

Turnover

Profit / Loss(balance sheet)

Classical TurnoverOrientation

• Profit Turnover-Ratio

Risk CapitalRisk Capital

EconomicResult

Value and Risk Oriented (Economical View on Return and Risk)

• Return on Risk Adjusted Capital (RORAC)

Source: Diers, Interne Unternehmensmodelle, ifa-Verlag Ulm, Germany

Management reacted to the altered prevailing conditions with a paradigm shift in corporate strategy developing from classical turnover orientation to value and risk based management in economic terms.

DFA model

DFA Model

Risk margin: Cost of Capital Background: MVM is the risk premium for an investor who has to finance risk capital; r(t) is risk free rate, CoC is the spread.

DFA model

+ 0,2 (gross) minus reinsurance effect of - 1,5 = -1,3

(assets)

Thank you for your attention !

Prof. Dr. Martin BalleerEuropean Actuarial Academy GmbHGeorg-August-Universität Göttingen

Germanymartin.balleer@actuarial-academy.com