Risk Exchange With Distorted Probabilities

The final version of this article appeared as: Tsanakas A., N. Christofides (2006), ''Risk exchange with distorted probabilities'', Astin Bulletin, 36(1), p.219-243.

26 Pages Posted: 13 Aug 2007 Last revised: 3 Jan 2014

See all articles by Andreas Tsanakas

Andreas Tsanakas

City University London - Cass Business School

Nikos Christofides

Imperial College London - Imperial College of Science, Technology and Medicine

Abstract

An exchange economy is considered, where agents (insurers/banks) trade risks. Decision making takes place under distorted probabilities, which are used to represent either rank-dependence of preferences or ambiguity with respect to real-world probabilities. Pricing formulas and risk allocations, generalising the results of Buhlmann (1980, 1984) are obtained via the construction of aggregate preferences from heterogeneous agents' utility and distortion functions. This involves the introduction of a novel 'collective ambiguity aversion' coefficient. It is shown that probability distortion changes insurers' behaviour, who trade not only to share the aggregate market risk, but are also found to bet against each other. Moreover, probability distortion tends to increase the price of insurance (increase asset returns). While the cases of rank-dependence and ambiguity are formally similar, an important distinction emerges as for rank-dependent preferences equilibria are determinate, while for ambiguity they are generally indeterminate.

Suggested Citation

Tsanakas, Andreas and Christofides, Nicos, Risk Exchange With Distorted Probabilities. The final version of this article appeared as: Tsanakas A., N. Christofides (2006), ''Risk exchange with distorted probabilities'', Astin Bulletin, 36(1), p.219-243.. Available at SSRN: https://ssrn.com/abstract=1006586 or http://dx.doi.org/10.2139/ssrn.1006586

Andreas Tsanakas (Contact Author)

City University London - Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Nicos Christofides

Imperial College London - Imperial College of Science, Technology and Medicine ( email )

Management School Centre for Quantitative Finance
London SW7 2BT
United Kingdom
+44 171 594 9165 (Phone)

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