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Finite-time ruin probabilities using bivariate Laguerre series

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  • Eric C. K. Cheung
  • Hayden Lau
  • Gordon E. Willmot
  • Jae-Kyung Woo

Abstract

In this paper, we revisit the finite-time ruin probability in the classical compound Poisson risk model. Traditional general solutions to finite-time ruin problems are usually expressed in terms of infinite sums involving the convolutions related to the claim size distribution and their integrals, which can typically be evaluated only in special cases where the claims follow exponential or (more generally) mixed Erlang distribution. We propose to tackle the partial integro-differential equation satisfied by the finite-time ruin probability and develop a new approach to obtain a solution in terms of bivariate Laguerre series as a function of the initial surplus level and the time horizon for a large class of light-tailed claim distributions. To illustrate the versatility and accuracy of our proposed method which is easy to implement, numerical examples are provided for claim amount distributions such as generalized inverse Gaussian, Weibull and truncated normal where closed-form convolutions are not available in the literature.

Suggested Citation

  • Eric C. K. Cheung & Hayden Lau & Gordon E. Willmot & Jae-Kyung Woo, 2023. "Finite-time ruin probabilities using bivariate Laguerre series," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2023(2), pages 153-190, February.
  • Handle: RePEc:taf:sactxx:v:2023:y:2023:i:2:p:153-190
    DOI: 10.1080/03461238.2022.2089051
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    Cited by:

    1. Denuit, Michel & Robert, Christian Y., 2023. "Conditional mean risk sharing of losses at occurrence time in the compound Poisson surplus model," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 23-32.

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