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A constraint-free approach to optimal reinsurance

Author

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  • Hans U. Gerber
  • Elias S.W. Shiu
  • Hailiang Yang

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.

Suggested Citation

  • Hans U. Gerber & Elias S.W. Shiu & Hailiang Yang, 2019. "A constraint-free approach to optimal reinsurance," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(1), pages 62-79, January.
    • Handle: RePEc:taf:sactxx:v:2019:y:2019:i:1:p:62-79
    DOI: 10.1080/03461238.2018.1488272
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    Cited by:

    1. Zaevski, Tsvetelin S. & Nedeltchev, Dragomir C., 2023. "From BASEL III to BASEL IV and beyond: Expected shortfall and expectile risk measures," International Review of Financial Analysis, Elsevier, vol. 87(C).

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