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Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims

Author

Listed:
  • Hansjörg Albrecher

    (Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Chamberonne Bâtiment Extranef, 1015 Lausanne, Switzerland)

  • Eleni Vatamidou

    (Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Chamberonne Bâtiment Extranef, 1015 Lausanne, Switzerland)

Abstract

We consider the Sparre Andersen risk process with interclaim times that belong to the class of distributions with rational Laplace transform. We construct error bounds for the ruin probability based on the Pollaczek–Khintchine formula, and develop an efficient algorithm to approximate the ruin probability for completely monotone claim size distributions. Our algorithm improves earlier results and can be tailored towards achieving a predetermined accuracy of the approximation.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:4:p:104-:d:276247
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    References listed on IDEAS

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    1. Willmot, Gordon E., 2007. "On the discounted penalty function in the renewal risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 17-31, July.
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    5. Hansjörg Albrecher & Hans Gerber & Hailiang Yang, 2010. "A Direct Approach to the Discounted Penalty Function," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(4), pages 420-434.
    6. 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.
    7. Landriault, David & Willmot, Gordon, 2008. "On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 600-608, April.
    8. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
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    Cited by:

    1. Tautvydas Kuras & Jonas Sprindys & Jonas Šiaulys, 2020. "Martingale Approach to Derive Lundberg-Type Inequalities," Mathematics, MDPI, vol. 8(10), pages 1-18, October.
    2. Josef Anton Strini & Stefan Thonhauser, 2020. "On Computations in Renewal Risk Models—Analytical and Statistical Aspects," Risks, MDPI, vol. 8(1), pages 1-20, March.

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