Geodesic
On the optimal reinsurance problem
Swen Kiesel 1   ; Ludger Rüschendorf 1
1 Department of Mathematical Stochastics University of Freiburg Eckerstraße 1 79104 Freiburg, Germany
Applicationes Mathematicae, Tome 40 (2013) no. 3, pp. 259-280 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am40-3-1
Keywords: paper consider optimal reinsurance problem endogenous form respect general convex risk measures varrho pricing rules means subdifferential formula compositions banach spaces first characterize optimal reinsurance contracts insurance taker insurer second step generalize characterization several insurance takers consequence obtain result saying cooperation brings risk compared insurance takers acting individually results extend previously known results literature

Swen Kiesel  1   ; Ludger Rüschendorf  1

1 Department of Mathematical Stochastics University of Freiburg Eckerstraße 1 79104 Freiburg, Germany 
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Swen Kiesel; Ludger Rüschendorf. On the optimal reinsurance problem. Applicationes Mathematicae, Tome 40 (2013) no. 3, pp. 259-280. doi: 10.4064/am40-3-1

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