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A saddlepoint approximation to the probability of ruin in the compound Poisson process with diffusion

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  • Gatto, Riccardo

Abstract

We provide a saddlepoint approximation which allows us to compute the probability of ruin of the risk process where the number of claims is Poisson distributed and where an additional Wiener term is considered. This approximation is very efficient and accurate. Some numerical illustrations and comparison with alternative methods are provided.

Suggested Citation

  • Gatto, Riccardo, 2008. "A saddlepoint approximation to the probability of ruin in the compound Poisson process with diffusion," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1948-1954, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1948-1954
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    References listed on IDEAS

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    1. Dufresne, François & Gerber, Hans U., 1989. "Three Methods to Calculate the Probability of Ruin," ASTIN Bulletin, Cambridge University Press, vol. 19(1), pages 71-90, April.
    2. Dufresne, Francois & Gerber, Hans U., 1991. "Risk theory for the compound Poisson process that is perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 51-59, March.
    3. Wang, Suojin, 1995. "One-step saddlepoint approximations for quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 65-74, July.
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    Cited by:

    1. He, Yue & Kawai, Reiichiro, 2022. "Moment and polynomial bounds for ruin-related quantities in risk theory," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1255-1271.

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