Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities
33 Pages Posted: 12 Aug 2007 Last revised: 3 Jan 2014
Abstract
The Aumann-Shapley (1974) value, originating in cooperative game theory, is used for the allocation of risk capital to portfolios of pooled liabilities, as proposed by Denault (2001). We obtain an explicit formula for the Aumann-Shapley value, when the risk measure is given by a distortion premium principle (Wang et al., 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 (1982), we discuss the role of Aumann-Shapley prices in an equilibrium context and present a simple numerical example.
Keywords: cooperative games, Aumann-Shapley value, distortion premium principle, coherent risk measures, equilibrium
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