Comonotonicity, Efficient Risk-Sharing and Equilibria in Markets with Short-Selling for Concave Law-Invariant Utilities
Dana, Rose-Anne (2011), Comonotonicity, Efficient Risk-Sharing and Equilibria in Markets with Short-Selling for Concave Law-Invariant Utilities, Journal of Mathematical Economics, 47, 3, p. 328-335. http://dx.doi.org/10.1016/j.jmateco.2010.12.016
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Economics
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Abstract (EN)In finite markets with short-selling, conditions on agents’ utilities insuring the existence of efficient allocations and equilibria are by now well understood. In infinite markets, a standard assumption is to assume that the individually rational utility set is compact. Its draw-back is that one does not know whether this assumption holds except for very few examples as strictly risk averse expected utility maximizers with same priors. The contribution of the paper is to show that existence holds for the class of strictly concave second order stochastic dominance preserving utilities. In our setting, it coincides with the class of strictly concave law-invariant utilities. A key tool of the analysis is the domination result of Lansberger and Meilijson that states that attention may be restricted to comonotone allocations of aggregate risk. Efficient allocations are characterized as the solutions of utility weighted problems with weights expressed in terms of the asymptotic slopes of the restrictions of agents’ utilities to constants. The class of utilities which is used is shown to be stable under aggregation.
Subjects / KeywordsPareto efficiency; law invariant utilities; comonotonicity; equilibria with short-selling; aggregation; representative agent
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