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A Markov Model for Loss Reserving

Published online by Cambridge University Press:  29 August 2014

Ole Hesselager
Ole Hesselager*
Affiliation:
University of Copenhagen, Denmark
*
Laboratory of Actuarial Mathematics, Universitetsparken 5, University of Copenhagen, DK-2100 Copenhagen Ø.
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Abstract

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The claims generating process for a non-life insurance portfolio is modelled as a marked Poisson process, where the mark associated with an incurred claim describes the development of that claim until final settlement. An unsettled claim is at any point in time assigned to a state in some state-space, and the transitions between different states are assumed to be governed by a Markovian law. All claims payments are assumed to occur at the time of transition between states. We develop separate expressions for the IBNR and RBNS reserves, and the corresponding prediction errors.

Keywords

IBNR and RBNS reservesmarked point processMarkov chainmartingale
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 2 , November 1994 , pp. 183 - 193
Copyright
Copyright © International Actuarial Association 1994

References

Andersen, P.K. and Borgan, Ø. (1985) Counting process models for life history data: A review (with discussion). Scan. Journ. Stat., 12, 97–158.Google Scholar
Arjas, E. (1989) The claims reserving problem in non-life insurance: Some structural ideas. ASTIN Bulletin 19, 139–152.CrossRefGoogle Scholar
Hachemeister, C.A. (1980) A stochastic model for loss reserving. Proceedings. ICA 1980, 185–194.Google Scholar
Norberg, R. (1992) Hattendorff's theorem and Thiele's differential equation generalized. Scand. Actuarial. J., 1992. 2–14.Google Scholar
Norberg, R. (1993) Prediction of outstanding liabilities in non-life insurance. ASTIN Bulletin 23, 95–115.CrossRefGoogle Scholar
Papatriandafyloy, A. and Waters, H.R. (1984) Martingales in life insurance. Scand. Actuarial J., 1984, 210–230.Google Scholar
Ramlau-Hamsen, H. (1988) Hattendorff s theorem: A Markov chain and counting process approach. Scand. Actuarial J., 1988, 143–156.Google Scholar