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Optimal risk allocation for convex risk functionals in general risk domains

Author

Listed:
  • Kiesel Swen

    (Department of Mathematical Stochastics, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany)

  • Rüschendorf Ludger

    (Department of Mathematical Stochastics, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany)

Abstract

In this paper, we formulate the classical optimal risk allocation problem for convex risk functionals defined on products of real Banach spaces as risk domains. This generality includes in particular the classical case of Lp risks but also allows to describe the influence of dependence in the risk allocation problem. We characterize optimal allocations and complete known existence and uniqueness results from the literature. We discuss in detail an application to expected risk functionals. This case can be dealt with by the Banach space approach applied to Orlicz hearts associated to the risk functionals. We give a detailed discussion of the necessary continuity and differentiability properties. Based on ordering results for Orlicz hearts we obtain extensions of the optimal allocation results to different Orlicz hearts as domain of risk functionals and establish a general form of the classical Borch theorem. In some numerical examples, optimal redistributions are determined for the expected risk case and the precision of the numerical calculation is checked.

Suggested Citation

  • Kiesel Swen & Rüschendorf Ludger, 2014. "Optimal risk allocation for convex risk functionals in general risk domains," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 335-365, December.
    • Handle: RePEc:bpj:strimo:v:31:y:2014:i:3-4:p:31:n:3
    DOI: 10.1515/strm-2012-1156
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    References listed on IDEAS

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