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Monte Carlo Methods for Insurance Risk Computation

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  • Shaul K. Bar-Lev
  • Ad Ridder

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 claim 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 modeling 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 importance sampling using an exponential change of measure. We conclude by numerical experiments of these algorithms, based on real car insurance claim data.

Suggested Citation

  • Shaul K. Bar-Lev & Ad Ridder, 2019. "Monte Carlo Methods for Insurance Risk Computation," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(3), pages 1-54, November.
    • Handle: RePEc:ibn:ijspjl:v:8:y:2019:i:3:p:54
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    References listed on IDEAS

    as
    1. Smyth, Gordon K. & Jørgensen, Bent, 2002. "Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 143-157, May.
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    Cited by:

    1. Sharifah Farah Syed Yusoff Alhabshi & Zamira Hasanah Zamzuri & Siti Norafidah Mohd Ramli, 2021. "Monte Carlo Simulation of the Moments of a Copula-Dependent Risk Process with Weibull Interwaiting Time," Risks, MDPI, vol. 9(6), pages 1-21, June.
    2. Shaul K. Bar-Lev & Apostolos Batsidis & Jochen Einbeck & Xu Liu & Panpan Ren, 2023. "Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    3. Shaul K. Bar-Lev & Ad Ridder, 2022. "The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk," Mathematics, MDPI, vol. 10(19), pages 1-25, October.

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    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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