modelling non-life insurance
TRANSCRIPT
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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
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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
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Modelling non-life insurance
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Corporate planning- A deterministic approach -
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Modelling non-life insurance
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Corporate planning
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Corporate planning
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Corporate planning
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Corporate planning
number of contracts
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Corporate planning
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Corporate planning
= costs of the claims managment
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Corporate planning
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Corporate planning
reserves that are estimated when claims are reported
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Corporate planning
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Corporate planning
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Corporate planning
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Corporate planning
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Corporate planning
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Modelling a company- A stochastic approach -
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Modelling non-life insurance
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Modelling non-life insurance
Economic result function
= technical cash-flow
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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.
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Modelling non-life insurance
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Modelling non-life insurance
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Modelling of claims
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Modelling non-life insurance
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Modelling non-life insurance
Claims modelling
It is useful to cluster claims in•Attritional•Large•CATclaims with regard to modelling
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Modelling non-life insurance
Stochastic modelling of claims
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Modelling non-life insurance
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Modelling of attritional claims (MTPL)-on Ultimate Basis –
Comment: „Ultimate Basis“ means that the final payments of claims are considered
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Modelling non-life insurance
Modelling attritional claims (MTPL)
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Modelling non-life insuranceModelling attritional claims (MTPL)
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Modelling non-life insurance
Separate modelling of claims frequeny and claims severity
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Modelling non-life insurance
Modelling of attritional claims frequency (1/3)
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Modelling non-life insuranceModelling of attritional claims frequency (2/3)
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Modelling non-life insurance
= 64,2 x 378.610
Modelling of attritional claims frequency (3/3)
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Modelling non-life insurance
Modelling of attritional claims average (1/2)
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Modelling non-life insuranceModelling of attritional claims average (2/2)
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Modelling non-life insurance
not presentedin this lecture
= 2820 x 24,3
Result: Modelling of attritional claims incurred in 2006
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Modelling large claims (MTPL)
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Modelling non-life insuranceModelling large claims
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Modelling non-life insuranceModelling large claims
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Modelling non-life insurance
over 3 years
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Modelling non-life insurance
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Modelling non-life insurance
(for 1 mio exposure)
backtesting:3,3 = 8,8 x 0,371
number of claims
= 8,8 x 378
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Modelling non-life insuranceModelling of large claims severity
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Modelling non-life insurance
= 3,3 x 1,919
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Modelling Building/CAT claims
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Modelling non-life insurance
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Modelling non-life insurance
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Modelling non-life insuranceModelling CAT claims
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Modelling non-life insurance
Modelling CAT claims
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Modelling non-life insurance
Modelling CAT claims
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Modelling non-life insurance
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DFA model„Feldafinger Brandkasse“
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DFA model
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DFA model
DFA = Dynamic Financial Analysis
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DFA model
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DFA model
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DFA model
DFA models are rather complex because of many simulations and many LOB and difficult to handle
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DFA model
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DFA model
following corporateplanning
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DFA model
Expected claims (total):
68,5 + 3,3x1,9 18= 74,8
see above
Distribution of severity losses CAT risks
CAT losses
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RBC ( = Risk Based Capital) calculationwithin DFA
Comment: RBC stands for the required capital; in Solvency II it is named SCR (Solvency Capital Requirement)
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DFA model
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DFA ModelRisk aggregationwithin Solvency II
Source: DAV-CERA Modul, Klassifizierung und Modellierung von Risiken
defaultmarket underwriting 1.aggregation
2. aggregation
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DFA model
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DFA model
RBC = TVAR - Mean
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DFA model
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DFA model
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DFA model
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DFA model
(building)
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DFA model
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DFA model
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DFA model
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DFA model
Reserving risk
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DFA model
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DFA model
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DFA model
Economic result: + 5,9 Mio €
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DFA model
(RBC)
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DFA model
Results on Company level
TVaR allocation method
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DFA model
(before RI and CoC)
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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.
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DFA model
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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.
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DFA model
+ 0,2 (gross) minus reinsurance effect of - 1,5 = -1,3
(assets)
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Thank you for your attention !
Prof. Dr. Martin BalleerEuropean Actuarial Academy GmbHGeorg-August-Universität Göttingen