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
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