Monte Carlo Methods for Insurance Risk Computation

Shaul Bar-Lev, Ad Ridder

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this paper we consider the problem of computing tail probabilities of the distribution of a random sum of positive random variables. We assume that the individual variables follow a reproducible natural exponential family (NEF) distribution, and that the random number has a NEF counting distribution with a cubic variance function. This specific modelling is supported by data of the aggregated claim distribution of an insurance company. Large tail probabilities are important as they reflect the risk of large losses, however, analytic or numerical expressions are not available. We propose several simulation algorithms which are based on an asymptotic analysis of the distribution of the counting variable and on the reproducibility property of the claim distribution. The aggregated sum is simulated efficiently by importancesampling using an exponential cahnge of measure. We conclude by numerical experiments of these algorithms.
Original languageEnglish
Pages (from-to)54-74
Number of pages21
JournalInternational Journal of Statistics and Probability
Volume8
Issue number3
Early online date24 Apr 2019
DOIs
Publication statusPublished - 2019

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Keywords

  • math.PR
  • 65C05, 91B30

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