Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-27T16:08:59.723Z Has data issue: false hasContentIssue false
  • English
  • Français

The Claims Reserving Problem in Non-Life Insurance: Some Structural Ideas

Published online by Cambridge University Press:  07 February 2018

Elja Arjas
Elja Arjas*
Affiliation:
University of Oulu, Finland
*
Department of Applied Mathematics and Statistics, University of Oulu, 90570 Oulu, Finland.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present some relatively simple structural ideas about how probabilistic modeling, and in particular, the modern theory of point processes and martingales, can be used in the estimation of claims reserves.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 19 , Issue 2 , November 1989 , pp. 139 - 152
Copyright
Copyright © International Actuarial Association 1989

References

Brémaud, P. (1981) Point Processes and Queues: Martingale Dynamics. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Bühlmann, H., Schnieper, R. and Straub, E. (1980) Claims reserves in casualty insurance based on a probabilistic model. Bulletin of the Association of Swiss Actuaries, 21–45.Google Scholar
Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation of Insurance Education, University of Pennsylvania, Philadelphia.Google Scholar
Hachemeister, C.A. (1980) A stochastic model for loss reserving. Transactions of the 21st International Congress of Actuaries 1, 185–194.Google Scholar
Jewell, W. S. (1980) Generalized models of insurance business. Report of Introduction. Transactions of the 21st International Congress of Actuaries S, 87–141.Google Scholar
Jewell, W. S. (1987) Predicting IBNYR events and delays I. Continuous time. Department of Industrial Engineering and Operations Research, University of California at Berkeley, Research Report.Google Scholar
Karr, A. F. (1986) Point Processes and Their Statistical Inference. Dekker, New York.Google Scholar
Linnemann, P. (1980) A multiplicative model for loss reserves: A stochastic process approach. University of Copenhagen, Laboratory of Actuarial Mathematics, Working Paper No. 32.Google Scholar
Norberg, R. (1986) A contribution to modelling of IBNR claims. Scandinavian Actuarial Journal 1986, 155–203.Google Scholar
Norros, I. (1985) Systems weakened by failures. Stochastic Processes Appl. 20, 181 196.CrossRefGoogle Scholar
Pentikäinen, T. and Rantala, J. (1986) Run-off risk as a part of claims fluctuation. ASTIN Bulletin 16, 113–147.CrossRefGoogle Scholar
Rantala, J. (1984) An application of stochastic control theory to insurance business. Acta Universitatis Tamperensis A, 164 (Academic dissertation).Google Scholar
Reid, D. H. (1981) A method of estimating outstanding claims in motor insurance with applications to experience rating. Colloque: Les mathematiques en Sciences Actuarielles-1981. Institut des Hautes Etudes de Belgique, Brussels, Belgium, 275–289.Google Scholar
Robbin, I. (1986) A Bayesian credibility formula for IBNR counts. Proceedings of the Cas. Actuarial Society Vol. LXXIII (1986), No. 139–140, 129–167 (with discussion).Google Scholar
Taylor, G.C. (1986) Claims Reserving in Non-Life Insurance. North-Holland, Amsterdam.Google Scholar
van Eeghen, J. (1981) Loss Reserving Methods. Surveys of Actuarial Studies No. 1, Nationale Nederlanden N.V. Google Scholar