Finite time ruin probabilities for tempered stable insurance risk processes

Philip S. Griffin, Ross A. Maller, Dale Roberts

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We study the probability of ruin before time t for the family of tempered stable Lévy insurance risk processes, which includes the spectrally positive inverse Gaussian processes. Numerical approximations of the ruin time distribution are derived via the Laplace transform of the asymptotic ruin time distribution, for which we have an explicit expression. These are benchmarked against simulations based on importance sampling using stable processes. Theoretical consequences of the asymptotic formulae indicate that some care is needed in the choice of parameters to avoid exponential growth (in time) of the ruin probabilities in these models. This, in particular, applies to the inverse Gaussian process when the safety loading is less than one.

Original languageEnglish (US)
Pages (from-to)478-489
Number of pages12
JournalInsurance: Mathematics and Economics
Volume53
Issue number2
DOIs
StatePublished - Sep 1 2013

Keywords

  • Convolution equivalent
  • Fluctuation theory
  • Insurance risk
  • Inverse Gaussian
  • Lévy process
  • Ruin probabilities
  • Tempered stable

ASJC Scopus subject areas

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

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