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Risks 2013, 1(3), 192-212; doi:10.3390/risks1030192
Article

Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach

1,*  and 2
Received: 6 November 2013 / Revised: 2 December 2013 / Accepted: 5 December 2013 / Published: 13 December 2013
(This article belongs to the Special Issue Application of Stochastic Processes in Insurance)
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Abstract

This paper is concerned with an insurance risk model whose claim process is described by a Lévy subordinator process. Lévy-type risk models have been the object of much research in recent years. Our purpose is to present, in the case of a subordinator, a simple and direct method for determining the finite time (and ultimate) ruin probabilities, the distribution of the ruin severity, the reserves prior to ruin, and the Laplace transform of the ruin time. Interestingly, the usual net profit condition will be essentially relaxed. Most results generalize those known for the compound Poisson claim process.
Keywords: Lévy subordinator; time reversal; ruin probability; (in)finite time horizon; ruin severity; reserves prior to ruin; ruin time Lévy subordinator; time reversal; ruin probability; (in)finite time horizon; ruin severity; reserves prior to ruin; ruin time
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Lefèvre, C.; Picard, P. Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach. Risks 2013, 1, 192-212.

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