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

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

1
Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, Bruxelles B-1050, Belgium
2
Institut de Science Financière et d'Assurances, Université de Lyon, 50 Avenue Tony Garnier, Lyon F-69007, France
*
Author to whom correspondence should be addressed.
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)
View Full-Text   |   Download PDF [340 KB, uploaded 13 December 2013]

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. View Full-Text
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 (CC BY 3.0).

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MDPI and ACS Style

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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