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
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.
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