Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities

33 Pages Posted: 12 Aug 2007 Last revised: 3 Jan 2014

See all articles by Andreas Tsanakas

Andreas Tsanakas

Bayes Business School (formerly Cass), City, University of London

Christopher Barnett

Imperial College London

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

Suggested Citation

Tsanakas, Andreas and Barnett, Christopher, Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities. The final version of this article appeared as: Tsanakas A., C. Barnett (2003), ''Risk capital allocation and cooperative pricing of insurance liabilities'', Insurance: Mathematics and Economics, 33(2), p.239-254., Available at SSRN: https://ssrn.com/abstract=1006635

Andreas Tsanakas (Contact Author)

Bayes Business School (formerly Cass), City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Christopher Barnett

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

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