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

• Main Authors: Claude Lefèvre, Philippe Picard
• Format: Article
• Language: English
• Published: MDPI AG 2013-12-01
• Series: Risks
• Subjects: Lévy subordinator; time reversal; ruin probability; (in)finite time horizon; ruin severity; reserves prior to ruin; ruin time
• Online Access: http://www.mdpi.com/2227-9091/1/3/192

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.