Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures

David J. Santana (), Juan González-Hernández () and Luis Rincón ()
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David J. Santana: IIMAS, UNAM
Juan González-Hernández: IIMAS, UNAM
Luis Rincón: UNAM

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 3, 775-798

Abstract: Abstract In this paper, we approximate the ultimate ruin probability in the Cramér-Lundberg risk model when claim sizes have an arbitrary continuous distribution. We propose two approximation methods, based on Erlang Mixtures, which can be used for claim sizes distribution both light and heavy tailed. Additionally, using a continuous version of the empirical distribution, we develop a third approximation which can be used when the claim sizes distribution is unknown and paves the way for a statistical application. Numerical examples for the gamma, Weibull and truncated Pareto distributions are provided.

Keywords: Ultimate ruin probability; Erlang mixture distribution; Continuous empirical distribution; Risk process; Classical risk model; 91B30; 62P05; 91B70 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-016-9515-6

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