A constraint-free approach to optimal reinsurance. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Gerber, Hans U.; Shiu, Elias S.W.; Yang, Hailiang
• Is Part Of: Scandinavian actuarial journal. Volume 2019:Issue 1(2019)
• Page Start: 62
• Page End: 79
• Publication Date: 2019-01-02
• Subjects: Optimal reinsurance -- expected utility -- convex premium principle -- Borch's theorem -- Pareto-optimal risk exchange -- constraint-free approach; Insurance, Life -- Mathematics -- Periodicals; Insurance -- Mathematics -- Periodicals; 368.01
• DOI: 10.1080/03461238.2018.1488272
• Languages: English
• ISSNs: 0346-1238

Abstract

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.