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

Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Methodology and Computing in Applied Probability Springer Journals

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

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Statistics; Statistics, general; Life Sciences, general; Electrical Engineering; Economics, general; Business and Management, general
ISSN
1387-5841
eISSN
1573-7713
D.O.I.
10.1007/s11009-016-9515-6
Publisher site
See Article on Publisher Site

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.

Journal

Methodology and Computing in Applied ProbabilitySpringer Journals

Published: Sep 17, 2016

References

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