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

Author

Listed:
  • David J. Santana

    (IIMAS, UNAM)

  • Juan González-Hernández

    (IIMAS, UNAM)

  • Luis Rincón

    (UNAM)

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.

Suggested Citation

  • David J. Santana & Juan González-Hernández & Luis Rincón, 2017. "Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 775-798, September.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:3:d:10.1007_s11009-016-9515-6
    DOI: 10.1007/s11009-016-9515-6
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    References listed on IDEAS

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    1. Gordon Willmot & Jae-Kyung Woo, 2007. "On the Class of Erlang Mixtures with Risk Theoretic Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(2), pages 99-115.
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    3. Krzysztof Burnecki & Marek Teuerle, 2010. "Ruin Probability in Finite Time," HSC Research Reports HSC/10/04, Hugo Steinhaus Center, Wroclaw University of Technology.
    4. Gzyl, Henryk & Novi-Inverardi, Pier-Luigi & Tagliani, Aldo, 2013. "Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 457-463.
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    7. Simon Lee & X. Lin, 2010. "Modeling and Evaluating Insurance Losses Via Mixtures of Erlang Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 107-130.
    8. Willmot, Gordon E., 1988. "Further use of Shiu's approach to the evaluation of ultimate ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 7(4), pages 275-281, December.
    9. Krzysztof Burnecki & Pawel Mista & Aleksander Weron, 2003. "A new De Vylder type approximation of the ruin probability in infinite time," HSC Research Reports HSC/03/05, Hugo Steinhaus Center, Wroclaw University of Technology.
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