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Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach
Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, Bruxelles B-1050, Belgium
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; in revised form: 2 December 2013 / Accepted: 5 December 2013 / Published: 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.
Keywords: Lévy subordinator; time reversal; ruin probability; (in)finite time horizon; ruin severity; reserves prior to ruin; ruin time
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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.
Lefèvre C, Picard P. Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach. Risks. 2013; 1(3):192-212.
Lefèvre, Claude; Picard, Philippe. 2013. "Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach." Risks 1, no. 3: 192-212.