On the efficient evaluation of ruin probabilities for completely monotone claim distributions

  • Authors:

  • Hansjörg Albrecher;Florin Avram;Dominik Kortschak

  • Affiliations:

  • Institute of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Dorigny, Batiment Extranef, CH-1015 Lausanne, Switzerland;Department de Mathematiques, Université de Pau, 64000, France;Institute of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Dorigny, Batiment Extranef, CH-1015 Lausanne, Switzerland

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

Quantified Score

Hi-index 7.29

Visualization

Abstract

In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed in [2]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical justification for the method. We also show that under weaker assumptions on the claim size distribution, the method may still perform reasonably well in some cases. This in particular provides an efficient alternative to a related method proposed in [3]. A number of numerical illustrations for the performance of this procedure is provided for both completely monotone and other types of random variables.