Optimal Risk Allocation in a Market with Non-Convex Preferences
18 Pages Posted: 13 Jun 2014
Date Written: June 11, 2014
The aims of this study are twofold. First, we consider an optimal risk allocation problem with non-convex preferences. By establishing an infimal representation for Choquet risk measures, we give some necessary and sufficient conditions for the existence of optimal and asymptotic optimal allocations. We will show that, similar to a market with convex preferences, in a non-convex framework with Choquet risk measures the boundedness of the optimal risk allocation problem depends only on the preferences. Second, we consider the same optimal allocation problem by adding a further assumption that allocations are co-monotone. We characterize the co-monotone optimal risk allocations within which we prove the “marginal risk allocations” take only the values zero and one. Remarkably, we can separate the role of the market preferences and the total risk in our representation.
Keywords: Non-convex preferences, Choquet risk measure, Optimal risk sharing problem
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