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Optimal insurance premium rates when the distribution of claims is unknown

Published online by Cambridge University Press:  14 July 2016

Itzhak Venezia
Itzhak Venezia*
Affiliation:
University of Rochester
*
∗ Permanent address: The Jerusalem School of Business, The Hebrew University, Jerusalem, Israel.
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Abstract

We analyze here the optimal premium rates for an insurance company for the case where the claims process is a stochastic process with unknown parameters. The beliefs of the insurance company about these parameters are represented by some prior distribution function, and the premium rates are determined on the basis of this distribution. The insurer learns about the unknown parameters from the past behavior of the claims process, and revises the prior distribution whenever new information is obtained (i.e., a claims stream is observed).

The learning process introduces multi-period dynamic considerations to the problem of the rate determination, since the rates determined at any period affect the claims process, and thus the information available for future decisions. We show how the optimal rates can be obtained by using some dynamic programming techniques. We also prove that the optimal rates obtained in our case are lower than those determined by an insurance company that does not revise its distribution.

Keywords

BAYESIAN REVISION OF INFORMATIONCOMPARISON OF EXPERIMENTSDYNAMIC PROGRAMMINGMARKOV DECISION PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 678 - 684
Copyright
Copyright © Applied Probability Trust 1979 

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References

Blackwell, D. (1951) Comparison of experiments. Proc. 2nd Berkeley Symp. Math. Statist. Prob., 93–102.Google Scholar
Blackwell, D. (1953) Equivalent comparisons of experiments. Ann. Math. Statist. 24, 265–273.Google Scholar
Borch, K. (1974) The Mathematical Theory of Insurance. Lexington, London.Google Scholar
Degroot, M. (1970) Optimal Statistical Decisions. McGraw-Hill, New York.Google Scholar
Marschak, J. and Miyasawa, K. (1968) Economic comparability of economic systems. Internat. Econom. Rev. 9, 137–174.Google Scholar
Mossin, J. (1968) Aspects of rational insurance purchasing. J. Political Econ. 76, 553–568.Google Scholar
Winkler, R. (1972) Introduction to Bayesian Inference and Decision. Holt, Rinehart and Winston, New York.Google Scholar