Comonotonicity, efficient risk-sharing and equilibria in markets with short-selling for concave law-invariant utilities
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 drawback 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.
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- Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999.
"On the Different Notions of Arbitrage and Existence of Equilibrium,"
Journal of Economic Theory,
Elsevier, vol. 87(1), pages 169-193, July.
- Dana, R.-A. & Le Van, C. & Magnien, F., 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Papiers d'Economie MathÃ©matique et Applications 1999.34, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Dana, Rose-Anne & Le Van, Cuong & Magnien, François, 1996. "On the different notions of arbitrage and existence of equilibrium," CEPREMAP Working Papers (Couverture Orange) 9616, CEPREMAP.
- repec:dau:papers:123456789/342 is not listed on IDEAS
- Cheng, Harrison H. C., 1991. "Asset market equilibrium in infinite dimensional complete markets," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 137-152.
- repec:dau:papers:123456789/2348 is not listed on IDEAS
- repec:dau:papers:123456789/6228 is not listed on IDEAS
- Grandmont, Jean-Michel, 1993.
"Temporary general equilibrium theory,"
Handbook of Mathematical Economics,
in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922
- Dana, Rose-Anne & Le Van, Cuong, 2000.
"Arbitrage, duality and asset equilibria,"
Journal of Mathematical Economics,
Elsevier, vol. 34(3), pages 397-413, November.
- Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
- Ludkovski, Michael & Rüschendorf, Ludger, 2008. "On comonotonicity of Pareto optimal risk sharing," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1181-1188, August.
- Florenzano, Monigue & Le Van, Cuong, 1986. "A note on the Gale-Nikaido-Debreu lemma and the existence of general equilibrium," Economics Letters, Elsevier, vol. 22(2-3), pages 107-110.
- Lars Tyge Nielsen, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Oxford University Press, vol. 56(3), pages 467-473.
- Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
- Page, Frank Jr., 1996. "Arbitrage and asset prices," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 183-208, June.
- Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-23, November.
- repec:dau:papers:123456789/6207 is not listed on IDEAS
- Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002.
"The geometry of arbitrage and the existence of competitive equilibrium,"
Journal of Mathematical Economics,
Elsevier, vol. 38(4), pages 373-391, December.
- Allouch, Nizar & Le Van, Cuong & Page, Jr. Frank H., 2001. "The geometry of arbitrage and the existence of competitive equilibrium," The Warwick Economics Research Paper Series (TWERPS) 598, University of Warwick, Department of Economics.
- Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
- G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 189-223, August.
- Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
- repec:dau:papers:123456789/361 is not listed on IDEAS
- Damir Filipović & Gregor Svindland, 2008. "Optimal capital and risk allocations for law- and cash-invariant convex functions," Finance and Stochastics, Springer, vol. 12(3), pages 423-439, July.
- Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "A necessary and sufficient condition for the compactness of individually rational and feasible outcomes and the existence of an equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 153-162, August.
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