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Risk Exchange with Distorted Probabilities

Published online by Cambridge University Press:  17 April 2015

Andreas Tsanakas  and
Nicos Christofides
Andreas Tsanakas
Affiliation:
Market Risk and Reserving Unit, Lloyd’s of London, One Lime Street, London EC3M 7HA, United Kingdom, E-mail: andreas.tsanakas@lloyds.com
Nicos Christofides
Affiliation:
Centre for Quantitative Finance, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom, E-mail: n.christofides@imperial.ac.uk
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Abstract

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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 Bühlmann (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.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 1 , May 2006 , pp. 219 - 243
Copyright
Copyright © ASTIN Bulletin 2006

Footnotes

*

The views expressed in this paper are solely those of the authors and do not necessarily reflect the views of Lloyd’s of London.

1

The authors are grateful to an anonymous referee for insightful suggestions that significantly improved the paper.

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