A+ CATEGORY SCIENTIFIC UNIT

On the optimal reinsurance problem

Volume 40 / 2013

Swen Kiesel, Ludger Rüschendorf Applicationes Mathematicae 40 (2013), 259-280 MSC: 91B30, 91G50. DOI: 10.4064/am40-3-1

Abstract

In this paper we consider the optimal reinsurance problem in endogenous form with respect to general convex risk measures $\varrho $ and pricing rules $\pi $. By means of a subdifferential formula for compositions in Banach spaces we first characterize optimal reinsurance contracts in the case of one insurance taker and one insurer. In the second step we generalize the characterization to the case of several insurance takers. As a consequence we obtain a result saying that cooperation brings less risk compared to insurance takers acting individually. Our results extend previously known results from the literature.

Authors

  • Swen KieselDepartment of Mathematical Stochastics
    University of Freiburg
    Eckerstraße 1
    79104 Freiburg, Germany
    e-mail
  • Ludger RüschendorfDepartment of Mathematical Stochastics
    University of Freiburg
    Eckerstraße 1
    79104 Freiburg, Germany
    e-mail

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