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

Author

Listed:
  • Claude Lefèvre

    (Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, Bruxelles B-1050, Belgium)

  • Philippe Picard

    (Institut de Science Financière et d'Assurances, Université de Lyon, 50 Avenue Tony Garnier, Lyon F-69007, France)

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.

Suggested Citation

  • Claude Lefèvre & Philippe Picard, 2013. "Ruin Time and Severity for a Lévy Subordinator Claim Process: A Simple Approach," Risks, MDPI, vol. 1(3), pages 1-21, December.
    • Handle: RePEc:gam:jrisks:v:1:y:2013:i:3:p:192-212:d:31342
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    References listed on IDEAS

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    8. Morales, Manuel, 2007. "On the expected discounted penalty function for a perturbed risk process driven by a subordinator," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 293-301, March.
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    Cited by:

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