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Volume 7
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10.3390/risks7040104
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Article

Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims

by
Hansjörg Albrecher
and
Eleni Vatamidou
*
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Chamberonne Bâtiment Extranef, 1015 Lausanne, Switzerland
*
Author to whom correspondence should be addressed.
Risks 2019, 7(4), 104; https://doi.org/10.3390/risks7040104
Submission received: 20 September 2019 / Revised: 7 October 2019 / Accepted: 8 October 2019 / Published: 14 October 2019
(This article belongs to the Special Issue Exit Problems for Lévy and Markov Processes with One-Sided Jumps and Related Topics)
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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.
Keywords: Sparre Andersen model; heavy tails; completely monotone distributions; error bounds; hyperexponential distribution Sparre Andersen model; heavy tails; completely monotone distributions; error bounds; hyperexponential distribution

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MDPI and ACS Style

Albrecher, H.; Vatamidou, E. Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims. Risks 2019, 7, 104. https://doi.org/10.3390/risks7040104

AMA Style

Albrecher H, Vatamidou E. Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims. Risks. 2019; 7(4):104. https://doi.org/10.3390/risks7040104

Chicago/Turabian Style

Albrecher, Hansjörg, and Eleni Vatamidou. 2019. "Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims" Risks 7, no. 4: 104. https://doi.org/10.3390/risks7040104

APA Style

Albrecher, H., & Vatamidou, E. (2019). Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims. Risks, 7(4), 104. https://doi.org/10.3390/risks7040104

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