Market-Consistent Actuarial ValuationIt is a challenging task to read the balance sheet of an insurance company. This derives from the fact that different positions are often measured by different yardsticks. Assets, for example, are mostly valued at market prices whereas liabilities are often measured by established actuarial methods. However, there is a general agreement that the balance sheet of an insurance company should be measured in a consistent way. Market-Consistent Actuarial Valuation presents powerful methods to measure liabilities and assets in a consistent way. The mathematical framework that leads to market-consistent values for insurance liabilities is explained in detail by the authors. Topics covered are stochastic discounting with deflators, valuation portfolio in life and non-life insurance, probability distortions, asset and liability management, financial risks, insurance technical risks, and solvency. |
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accounting principle actuarial asset portfolio assume Assumption 2.16 Assumption 5.3 balance sheet best-estimate reserves Black–Scholes Bühlmann cash flow choose Ci,J CL method claims payments claims reserving coherent risk measure conditional expectations conditional MSEP Corollary cost-of-capital coupon bond prices define deflator denotes described deterministic equivalent martingale measure example expected shortfall filtered probability space financial instruments financial market financial mathematics financial risks gamma-gamma BCL model given implies insurance company insurance liabilities insurance technical risks Lemma linear log-normal distribution Mack’s Margrabe option Merz–Wüthrich nominal non-informative prior limit non-life insurance number of units numeraire order life table outstanding liabilities parameter prediction uncertainty premium price process probability distortion probability measure protected against insurance pure claim put option random variable reinsurance replicate risk measure Sect Solvency II span-deflator ULAE payments Valuation Portfolio Valuation Scheme VaPo protected VaPo(X vector Wüthrich zero coupon bond