Market-Consistent Actuarial Valuation (Google eBook)
Springer Science & Business Media, Sep 2, 2010 - Actuarial science - 168 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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accident accounting principle actuarial assume Assumption 2.15 B¨uhlmann beneﬁt calculate cash ﬂow choose claims reserving conditional expectations Corollary deﬁne deﬁnition deﬂator denotes deterministic diﬀerent equivalent martingale measure Esscher example expected shortfall F-adapted ﬁnancial instruments ﬁnancial market ﬁnancial risks ﬁrst ﬁxed function given Hence Henceforth i+j=t implies insurance company insurance liabilities insurance technical risks interest rate Lemma linear loading loss lt+k Margrabe option Market-Consistent Actuarial Valuation market-consistent values martingale monetary value Moreover non-life insurance number of units numeraire obtain order life table parameter estimation error prediction premium price processes probability distortion probability measure probability space protected against insurance random variable reinsurance Remark risk aversion risk measure risk neutral measure risk neutral valuation solvency stochastic target capital ULAE valuation portfolio protected VaPo protected VaPo(T+1 VaPo(X Vasicek model W¨uthrich Wiener process Xt+i Xt+k zero coupon bond