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Bayesian estimation of finite time ruin probabilities

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  • M. Concepcion Ausin
  • Michael P. Wiper
  • Rosa E. Lillo

Abstract

In this paper, we consider Bayesian inference and estimation of finite time ruin probabilities for the Sparre Andersen risk model. The dense family of Coxian distributions is considered for the approximation of both the inter‐claim time and claim size distributions. We illustrate that the Coxian model can be well fitted to real, long‐tailed claims data and that this compares well with the generalized Pareto model. The main advantage of using the Coxian model for inter‐claim times and claim sizes is that it is possible to compute finite time ruin probabilities making use of recent results from queueing theory. In practice, finite time ruin probabilities are much more useful than infinite time ruin probabilities as insurance companies are usually interested in predictions for short periods of future time and not just in the limit. We show how to obtain predictive distributions of these finite time ruin probabilities, which are more informative than simple point estimations and take account of model and parameter uncertainty. We illustrate the procedure with simulated data and the well‐known Danish fire loss data set. Copyright © 2009 John Wiley & Sons, Ltd.

Suggested Citation

  • M. Concepcion Ausin & Michael P. Wiper & Rosa E. Lillo, 2009. "Bayesian estimation of finite time ruin probabilities," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 787-805, November.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:6:p:787-805
    DOI: 10.1002/asmb.762
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. Avram, F. & Usábel, M., 2004. "Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 315-332, November.
    3. M. J. Faddy, 1994. "Examples of fitting structured phase–type distributions," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 10(4), pages 247-255.
    4. Cairns, Andrew J. G., 2000. "A discussion of parameter and model uncertainty in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 313-330, December.
    5. Avram, Florin & Usabel, Miguel, 2003. "Finite time ruin probabilities with one Laplace inversion," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 371-377, July.
    6. Thorin, Olof & Wikstad, Nils, 1973. "Numerical evaluation of ruin probabilities for a finite period," ASTIN Bulletin, Cambridge University Press, vol. 7(2), pages 137-153, September.
    7. Dickson, David C. M. & Drekic, Steve, 2004. "The joint distribution of the surplus prior to ruin and the deficit at ruin in some Sparre Andersen models," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 97-107, February.
    8. Asmussen, Soren & Avram, Florin & Usabel, Miguel, 2002. "Erlangian Approximations for Finite-Horizon Ruin Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 267-281, November.
    9. Hipp, Christian, 1989. "Estimators and Bootstrap Confidence Intervals for Ruin Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 19(1), pages 57-70, April.
    10. Ausin, M. Concepcion & Wiper, Michael P. & Lillo, Rosa E., 2008. "Bayesian prediction of the transient behaviour and busy period in short- and long-tailed GI/G/1 queueing systems," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1615-1635, January.
    11. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
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    Cited by:

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    2. Macci, Claudio & Torrisi, Giovanni Luca, 2011. "Risk processes with shot noise Cox claim number process and reserve dependent premium rate," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 134-145, January.

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