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Risk capital allocation and cooperative pricing of insurance liabilities. (English) Zbl 1103.91317

Summary: The Aumann–Shapley value [R. J. Aumann and L. S. Shapley, Values of non-atomic games, Princeton Univ. Press, Princeton, N.J. (1974; Zbl 0311.90084)], originating in cooperative game theory, is used for the allocation of risk capital to portfolios of pooled liabilities, as proposed by Denault [Coherent allocation of risk capital, J. Risk 4, No. 1, 1 (2001)]. We obtain an explicit formula for the Aumann–Shapley value, when the risk measure is given by a distortion premium principle [Axiomatic characterisation of insurance prices, Insur. Math. Econ. 21, No. 2, 173 (1997)]. The capital allocated to each instrument or (sub)portfolio is given as its expected value under a change of probability measure. Motivated by Mirman and Tauman [Demand compatible equitable cost sharing prices, Math. Oper. Res. 7, No. 1, 40 (1982)], we discuss the role of Aumann–Shapley prices in an equilibrium context and present a simple numerical example.

MSC:

91A12 Cooperative games
91B30 Risk theory, insurance (MSC2010)

Citations:

Zbl 0311.90084
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