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Optimal Reinsurance and Dividend Payment Strategies*

Published online by Cambridge University Press:  29 August 2014

Pantelis M. Pechlivanides
Pantelis M. Pechlivanides*
Affiliation:
National Technical University, Athens
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This paper presents a normative model for the sequential reinsurance and dividend-payment problem of the Insurance Company (I.C.). Optimal strategies are found in closed form for a class of utility functions. In some sense the model studied can be viewed as an adaptation of Hakansson's investment-consumption model of the individual [3] or a generalization of Frisque's model for the dynamic management of an I.C. [2].

In Section 2 the model is formulated as a discrete time dynamic programming problem. The objective of the I.C. is assumed to be maximization of the expected utility of the dividend streams paid to stock/policy-holders (s/p-holders). The initial reserves level is assumed to be known. The premiums to be collected in each period for selling policies are known in advance. The losses due to claims from policy-holders are random variables independent from period to period. In each period the I.C. must decide on the portion of the reserves to be paid as dividends and on the form and level of reinsurance with a reinsurer that quotes prices for any contract.

Optimal strategies in closed form are found in Section 3 when the utility function of the I.C. is given by the discounted sum of one-period utilities of dividends; and when the one-period utilities belong to the linear risk-tolerance class, which is given by: (la) u(x) = (ax + b)c+1/a(c + 1); ax + b > o, ac < o. (Ib) u(x) = log(ax + b); ax + b > o. (II) u(x) = — eγx; γ > o.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 10 , Issue 1 , May 1978 , pp. 34 - 46
Copyright
Copyright © International Actuarial Association 1978

Footnotes

*

This study is based on my Ph.D. thesis submitted to the University of California, Berkeley (1975). I am grateful to Professor W. S. Jewell (Chairman) as well as to Professors Nils Hakansson and David Gale for many helpful comments and criticisms.

References

REFERENCES

[1] Arrow, K., 1971. Essays in the Theory of Risk Bearing, North-Holland.Google Scholar
[2] Frisque, A., 1974. “Dynamic Model of Insurance Company's Management,” ASTIN, Vol. 8, part 1.Google Scholar
[3] Hakansson, N., 1970. “Optimal Investment and Consumption Strategies under Risk for a Class of Utility Functions,” Econometvica, Vol. 38, No. 5.Google Scholar
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[5] Meyer, R., 1969. “On the Relationship Among the Utility of Assets, the Utility of Consumption and Investment Strategy,” Proceedings of the 5th International Conference of Operations Research.Google Scholar
[6] Pechlivanides, P., 1975. “Reinsurance Market Mechanisms and Dividend Strategies for an Insurance Company,” Ph.D. Thesis published as an Operations Research Center Report, ORC 75-17, University of California, Berkeley.Google Scholar
[7] Pratt, J., 1964. “Risk Aversion in the Small and in the Large,” Econometrica, Vol. 32, No. 1–2.CrossRefGoogle Scholar