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Higher-order expansions for compound distributions and ruin probabilities with subexponential claims

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  • Hansjörg Albrecher
  • Christian Hipp
  • Dominik Kortschak

Abstract

Let X i (i=1,2, …) be a sequence of subexponential positive independent and identically distributed random variables. In this paper, we offer two alternative approaches to obtain higher-order expansions of the tail of and subsequently for ruin probabilities in renewal risk models with claim sizes X i . In particular, these emphasize the importance of the term for the accuracy of the resulting asymptotic expansion of . Furthermore, we present a more rigorous approach to the often suggested technique of using approximations with shifted arguments. The cases of a Pareto type, Weibull and Lognormal distribution for X i are discussed in more detail and numerical investigations of the increase in accuracy by including higher-order terms in the approximation of ruin probabilities for finite realistic ranges of s are given.

Suggested Citation

  • Hansjörg Albrecher & Christian Hipp & Dominik Kortschak, 2010. "Higher-order expansions for compound distributions and ruin probabilities with subexponential claims," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2010(2), pages 105-135.
    • Handle: RePEc:taf:sactxx:v:2010:y:2010:i:2:p:105-135
    DOI: 10.1080/03461230902722726
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