Market-Consistent Actuarial Valuation
Springer Science & Business Media, Sep 2, 2010 - Mathematics - 157 pages
It 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 assume Assumption 2.15 best-estimate Bühlmann calculate cash flow chain-ladder factors choose Ci,j claims payments claims reserving conditional expectations Corollary cost-of-capital define denotes deviation equivalent martingale measure Esscher example expected shortfall F-adapted financial instruments financial market financial mathematics financial risks function given Hence Henceforth implies independent insurance company insurance liabilities insurance technical risks interest rate Lemma linear loading loss lt+k Margrabe option Market-Consistent Actuarial Valuation market-consistent values monetary value Moreover non-life insurance number of units numeraire obtain order life table parameter estimation error prediction premium probability distortion probability measure protected against insurance put option random variable reinsurance Remark risk aversion risk measure risk neutral measure self-financing property solvency span-deflator target capital ULAE V(t)t+k ValPo valuation portfolio protected VaPo VaPo protected VaPo(T+1 VaPo(X Vasicek model vector Wiener process Wüthrich zero coupon bond