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A Class of Conjugate Priors with Applications to Excess-of-Loss Reinsurance

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  • Hesselager, Ole

Abstract

We consider the problem of forecasting the total cost of claims in excess-of-loss reinsurance. The number of claims reported to the direct insurer is assumed to follow a Poisson law, and the claim severities are modelled by a Pareto distribution. The Poisson frequency as well as the Pareto parameter will be considered as random parameters in a Bayesian setting. We derive the class of conjugate joint prior distributions, which turn out to specify a (prior) dependence between the two parameters. The use of conjugate priors facilitates the mathematical analysis, and it also makes it easy to interpret the parameters of the prior distribution.

Suggested Citation

  • Hesselager, Ole, 1993. "A Class of Conjugate Priors with Applications to Excess-of-Loss Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 77-93, May.
    • Handle: RePEc:cup:astinb:v:23:y:1993:i:01:p:77-93_00
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    Cited by:

    1. Pai, Jeffrey S., 1997. "Bayesian analysis of compound loss distributions," Journal of Econometrics, Elsevier, vol. 79(1), pages 129-146, July.
    2. Mauricio Diaz & Daniel M. Frances, 2014. "Bayesian Inference Using Gibbs Sampling in Applications and Curricula of Decision Analysis," INFORMS Transactions on Education, INFORMS, vol. 14(2), pages 86-95, February.
    3. Ali Karimnezhad & Ahmad Parsian, 2014. "Robust Bayesian methodology with applications in credibility premium derivation and future claim size prediction," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 287-303, July.
    4. Hurlimann, Werner, 1995. "Predictive stop-loss premiums and Student's t-distribution," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 151-159, May.

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