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Ultimate Ruin Probabilities for Generalized Gamma-Convolutions Claim Sizes

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  • Usábel, M.

Abstract

A method of inverting the Laplace transform based on the integration between zeros technique and a simple acceleration algorithm is presented. This approach was designed to approximate ultimate ruin probabilities for Γ-convolutions claim sizes, but it can be also used with other distributions. The stable algorithm obtained yields interval approximations (lower and upper bounds) to any desired degree of accuracy even for very large values of u (1,000,000), initial reserves, without increasing the number of computations. This last fact can be considered an interesting property compared with other recursive methods previously used in actuarial literature or other methods of inverting Laplace transforms.

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  • Usábel, M., 2001. "Ultimate Ruin Probabilities for Generalized Gamma-Convolutions Claim Sizes," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 59-79, May.
    • Handle: RePEc:cup:astinb:v:31:y:2001:i:01:p:59-79_00
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    Cited by:

    1. Pawel Mista, 2006. "Analytical and numerical approach to corporate operational risk modelling," HSC Research Reports HSC/06/03, Hugo Steinhaus Center, Wroclaw University of Technology.

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