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Bayesian Estimation of Outstanding Claim Reserves

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  • Enrique de Alba

Abstract

This paper presents a Bayesian approach to forecasting outstanding claims, either the total number of claims or the total amount, that is used for claims reserving. The assumption is made that there is complete information for one or two past years of origin and partial information for some development years of other years of origin. It also assumes payments are made annually and that the development of partial payments follows a stable payoff pattern from one year of origin to another. Two different models are presented: one for the number of claims (intensity) and one for claim amounts (severity). The advantage of using this procedure is that actuaries can derive the complete predictive distribution of the reserve requirements, from which, in turn, it is possible to obtain point estimates as well as probability intervals and other summary measures, such as mean, variance, and quantiles.

Suggested Citation

  • Enrique de Alba, 2002. "Bayesian Estimation of Outstanding Claim Reserves," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(4), pages 1-20.
    • Handle: RePEc:taf:uaajxx:v:6:y:2002:i:4:p:1-20
    DOI: 10.1080/10920277.2002.10596060
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    Cited by:

    1. Alice X. D. Dong & Jennifer S. K. Chan & Gareth W. Peters, 2014. "Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression," Papers 1402.2492, arXiv.org.
    2. Klaus Schmidt, 2012. "Loss prediction based on run-off triangles," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 265-310, June.
    3. Han, Zhongxian & Gau, Wu-Chyuan, 2008. "Estimation of loss reserves with lognormal development factors," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 389-395, February.
    4. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2016. "Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 63-78.
    5. Gigante, Patrizia & Picech, Liviana & Sigalotti, Luciano, 2013. "Claims reserving in the hierarchical generalized linear model framework," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 381-390.
    6. Bente Corneliu Cristian & Gavriletea Marius Dan, 2015. "Inflation Adjusted Chain Ladder Method," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 370-379, December.
    7. Dong, A.X.D. & Chan, J.S.K., 2013. "Bayesian analysis of loss reserving using dynamic models with generalized beta distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 355-365.
    8. Luca Regis, 2011. "A Bayesian copula model for stochastic claims reserving," Carlo Alberto Notebooks 227, Collegio Carlo Alberto.

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