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Approximation of ruin probabilities via Erlangized scale mixtures

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  • Peralta, Oscar
  • Rojas-Nandayapa, Leonardo
  • Xie, Wangyue
  • Yao, Hui

Abstract

In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale mixtures (ESM) that correspond to nonnegative and absolutely continuous distributions which can be written as a Mellin–Stieltjes convolution Π⋆G of a nonnegative distribution Π with an Erlang distribution G. A distinctive feature of such a class is that it contains heavy-tailed distributions.

Suggested Citation

  • Peralta, Oscar & Rojas-Nandayapa, Leonardo & Xie, Wangyue & Yao, Hui, 2018. "Approximation of ruin probabilities via Erlangized scale mixtures," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 136-156.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:136-156
    DOI: 10.1016/j.insmatheco.2017.12.005
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    References listed on IDEAS

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    1. Vatamidou, E. & Adan, I.J.B.F. & Vlasiou, M. & Zwart, B., 2013. "Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 366-378.
    2. Ramsay, Colin M., 2003. "A solution to the ruin problem for Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 109-116, August.
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    Cited by:

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    2. Hansjörg Albrecher & Eleni Vatamidou, 2019. "Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims," Risks, MDPI, vol. 7(4), pages 1-14, October.

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