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Claims Reserving in Continuous Time; A Nonparametric Bayesian Approach

Published online by Cambridge University Press:  29 August 2014

Svend Haastrup  and
Elja Arjas
Svend Haastrup
Affiliation:
Laboratory of Actuarial Mathematics, Universitetsparken 5, 2100 København Ø, Denmark
Elja Arjas
Affiliation:
Department of Applied Mathematics and Statistics, University of Oulu, Linnanmaa 90570, Oulu, Finland
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Abstract

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Occurrences and developments of claims are modelled as a marked point process. The individual claim consists of an occurrence time, two covariates, a reporting delay, and a process describing partial payments and settlement of the claim. Under certain likelihood assumptions the distribution of the process is described by 14 one-dimensional components. The modelling is nonparametric Bayesian. The posterior distribution of the components and the posterior distribution of the outstanding IBNR and RBNS liabilities are found simultaneously. The method is applied to a portfolio of accident insurances.

Keywords

IBNR and RBNS liabilitiesmarked point processmissing dataMarkov chain Monte Carlo
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 2 , November 1996 , pp. 139 - 164
Copyright
Copyright © International Actuarial Association 1996

References

Arjas, E. 1989. The claim reserving problem in non-life insurance: some structural ideas. ASTIN Bull. Vol. 19, no. 2, 139–152.Google Scholar
Arjas, E., Gasbarra, D. 1994. Nonparametric Bayesian inference from right censored survival data using the Gibbs sampler. Statistica Sinica, 4, 505–524.Google Scholar
Hesselager, O. 1994. A Markov model for loss reserving. ASTIN Bull. Vol. 24, no. 2, 183–193.Google Scholar
Jewell, W.S. 1989. Predicting IBNYR events and delays I. Continuous time. ASTIN Bull. Vol. 19, no. 1, 25–56.Google Scholar
Karr, A. 1991. Point processes and their statistical inference. Marcel Dekker Inc.Google Scholar
Kirkegaard, T. 1994. Praktisk anvendelse af en reservemodel på ulykkesforsikringer. Master's thesis (in Danish), University of Copenhagen.Google Scholar
Norberg, R. 1993a. Prediction of outstanding liabilities in non-life insurance. ASTIN Bull. Vol. 23. no. I, 95–115.Google Scholar
Norberg, R. 1993b. Prediction of outstanding liabilities: model variations and extensions. Unpublished.Google Scholar
Norberg, R. 1993c. Prediction of outstanding liabilities: parameter estimation. Proceedings of the XXIV ASTIN Coll., 255–266.Google Scholar
Smith, A.F.M., Roberts, G.O. 1993. Bayesian computations via the Gibbs sampler and related Markov chain Monte Carlo methods. J. R. Statist. Soc. B, Vol. 55, no. 1, 3–23.Google Scholar
Tierney, L. 1994. Markov chains for exploring posterior distributions (with discussions). Annals of Statistics. Vol. 22, no. 4, 1701–1762.Google Scholar