Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria
This paper is concerned with the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk. We deal with the problem by exploring the relationship between maximizing the adjustment coefficient and maximizing the expected utility of wealth for the exponential utility function, both with respect to the retained risk of the insurer. Assuming that the premium calculation principle is a convex functional and that some other quite general conditions are fulfilled, we prove the existence and uniqueness of solutions and provide a necessary optimal condition. These results are used to find the optimal reinsurance policy when the reinsurance premium calculation principle is the expected value principle or the reinsurance loading is an increasing function of the variance. In the expected value case the optimal form of reinsurance is a stop-loss contract. In the other cases, it is described by a nonlinear function.
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- Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
- Centeno, Maria de Lourdes, 1997. "Excess of Loss Reinsurance and the Probability of Ruin in Finite Horizon," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 27(01), pages 59-70, May.
- Vajda, Stefan, 1962. "Minimum Variance Reinsurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 2(02), pages 257-260, September.
- Ohlin, Jan, 1969. "On a class of measures of dispersion with application to optimal reinsurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 5(02), pages 249-266, May.
- Kahn, Paul Markham, 1961. "Some Remarks on a Recent Paper by Borch," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 1(05), pages 265-272, July.
- anonymous, 1991. "Fed upgrades functional cost analysis program," Financial Update, Federal Reserve Bank of Atlanta, issue Win, pages 1-2,6.
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