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Characterization of optimal risk allocations for convex risk functionals

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  • Kiesel Swen

    (University of Freiburg, Department of Math. Stochastics, Freiburg, Deutschland)

  • Rüschendorf Ludger

Abstract

In this paper we consider the problem of optimal risk allocation or risk exchange with respect to convex risk functionals, which not necessarily are monotone or cash invariant. General existence and characterization results are given for optimal risk allocations minimizing the total risk as well as for Pareto optimal allocations. We establish a general uniqueness result for optimal allocations. As particular consequence we obtain in case of cash invariant, strictly convex risk functionals the uniqueness of Pareto optimal allocations up to additive constants. In the final part some tools are developed useful for the verification of the basic intersection condition made in the theorems which are applied in several examples.

Suggested Citation

  • Kiesel Swen & Rüschendorf Ludger, 2009. "Characterization of optimal risk allocations for convex risk functionals," Statistics & Risk Modeling, De Gruyter, vol. 26(4), pages 303-319, July.
    • Handle: RePEc:bpj:strimo:v:26:y:2009:i:4:p:303-319:n:1
    DOI: 10.1524/stnd.2008.1001
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    References listed on IDEAS

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    1. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
    2. Burgert, Christian & Rüschendorf, Ludger, 2008. "Allocation of risks and equilibrium in markets with finitely many traders," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 177-188, February.
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    5. Bühlmann, Hans & Jewell, William S., 1979. "Optimal Risk Exchanges," ASTIN Bulletin, Cambridge University Press, vol. 10(3), pages 243-262, December.
    6. Beatrice Acciaio, 2007. "Optimal risk sharing with non-monotone monetary functionals," Finance and Stochastics, Springer, vol. 11(2), pages 267-289, April.
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