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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

Type
Article accepté pour publication ou publié
Date
2011
Journal name
Journal of Mathematical Economics
Volume
47
Number
3
Publisher
Elsevier
Pages
328-335
Publication identifier
http://dx.doi.org/10.1016/j.jmateco.2010.12.016
Metadata
Show full item record
Author(s)
Dana, Rose-Anne
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 / Keywords
Pareto efficiency; law invariant utilities; comonotonicity; equilibria with short-selling; aggregation; representative agent
JEL
G1 - General Financial Markets

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