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Prediction of Outstanding Liabilities in Non-Life Insurance1

Published online by Cambridge University Press:  29 August 2014

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

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A fully time-continuous approach is taken to the problem of predicting the total liability of a non-life insurance company. Claims are assumed to be generated by a non-homogeneous marked Poisson process, the marks representing the developments of the individual claims. A first basic result is that the total claim amount follows a generalized Poisson distribution. Fixing the time of consideration, the claims are categorized into settled, reported but not settled, incurred but not reported, and covered but not incurred. It is proved that these four categories of claims can be viewed as arising from independent marked Poisson processes. By use of this decomposition result predictors are constructed for all categories of outstanding claims. The claims process may depend on observable as well as unobservable risk characteristics, which may change in the course of time, possibly in a random manner. Special attention is given to the case where the claim intensity per risk unit is a stationary stochastic process. A theory of continuous linear prediction is instrumental.

Keywords

Claims reservesmarked Poisson processstochastic claims intensitylinear prediction
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 23 , Issue 1 , May 1993 , pp. 95 - 115
Copyright
Copyright © International Actuarial Association 1993

Footnotes

1

Based on invited paper presented at the 23rd ASTIN Colloquium, Stockholm, 1991.

References

REFERENCES

Arjas, E. (1989) The claims reserving problem in non-life insurance — some structural ideas. ASTIN Bulletin 19, 139–152.CrossRefGoogle Scholar
Beard, R., Pentikäinen, T. and Pesonen, E. (1984) Risk Theory. Chapman and Hall, New York.CrossRefGoogle Scholar
Hesselager, O. and Witting, T. (1988) A credibility model with random fluctuations in delay probabilities for the prediction of IBNR claims. ASTIN Bulletin 18, 79–90.CrossRefGoogle Scholar
Jewell, W.S. (1989) Predicting IBNYR events and delays I. Continuous time. ASTIN Bulletin 19, 25–55.CrossRefGoogle Scholar
Karlsson, J.E. (1976) The expected value of IBNR-claims. Scand. Actuarial J., 1976, 108–110.Google Scholar
Neuhaus, W. (1992) IBNR models with random delay distributions. To appear in Scand. Actuarial J.CrossRefGoogle Scholar
Norberg, R. and Sundt, B. (1985) Draft of a system for solvency control in non-life insurance. ASTIN Bulletin 15, 149–169.CrossRefGoogle Scholar
Norberg, R. (1986) A contribution to modelling of IBNR claims. Scand. Actuarial J., 1986, 155–203.CrossRefGoogle Scholar
Norberg, R. (1989) A strategy for solvency control. Paper presented to the 21st ASTIN Colloquium, NewYork, November 1989.Google Scholar
Norberg, R. (1992) Linear estimation and credibility in continuous time. ASTIN Bulletin 22, 149–165.CrossRefGoogle Scholar