A constraint-free approach to optimal reinsurance |
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Authors: | Hans U Gerber Elias SW Shiu |
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Institution: | 1. Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong;2. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Lausanne, Switzerland;3. Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA, USA |
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Abstract: | Reinsurance is available for a reinsurance premium that is determined according to a convex premium principle H. The first insurer selects the reinsurance coverage that maximizes its expected utility. No conditions are imposed on the reinsurer's payment. The optimality condition involves the gradient of H. For several combinations of H and the first insurer's utility function, closed-form formulas for the optimal reinsurance are given. If H is a zero utility principle (for example, an exponential principle or an expectile principle), it is shown, by means of Borch's Theorem, that the optimal reinsurer's payment is a function of the total claim amount and that this function satisfies the so-called 1-Lipschitz condition. Frequently, authors impose these two conclusions as hypotheses at the outset. |
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Keywords: | Optimal reinsurance expected utility convex premium principle Borch's theorem Pareto-optimal risk exchange constraint-free approach |
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