Edgeworth type expansion of ruin probability under Lévy risk processes in the small loading asymptotics

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Abstract

This paper presents an asymptotic expansion of the ultimate ruin probability under Lévy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for compound geometric distributions. We give higher-order expansion of the ruin probability, any order of which is available in explicit form, and discuss a certain type of validity of the expansion. We shall also give applications to evaluation of the VaR-type risk measure due to ruin, and the scale function of spectrally negative Lévy processes.

Original languageEnglish
Pages (from-to)620-648
Number of pages29
JournalScandinavian Actuarial Journal
Issue number7
DOIs
Publication statusPublished - 2014 Oct
Externally publishedYes

Keywords

  • Edgeworth type expansion
  • Lévy insurance risk
  • compound geometric sum
  • ruin probability
  • small safety loading

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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