Improved Approximations for the Aggregate Claims Distribution in the Individual Model

Christian Hipp

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Probability and Risk Models Probability and Statistical Research Insurance, Mortality, Demography, Risk Management

Abstract

Abstract Kornya-type higher order approximations are derived for the aggregate claims distribution and for stop loss premiums in the individual model with arbitrary positive claims. Absolute error bounds and error bounds based on concentration functions are given. In the Gerber portfolio containing 31 policies, second order approximations lead to an accuracy of 3 × 10 −4 , and third order approximations to 1.7 ×10 −5 .

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1979An introduction to mathematical risk theory 1981Recursive Evaluation of a Family of Compound Distributions

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1989The Aggregate Claims Distribution in the Individual Model with Arbitrary Positive Claims 1994On a class of approximative computation methods in the individual risk model 1990Approximation of sums by compound Poisson distributions with respect to stop-loss distances 2002Recursive evaluation of aggregate claims distributions 1992Error Bounds for Compound Poisson Approximations of the Individual Risk Model

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