No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity
The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. A sufficient condition for existence of efficient allocations is that the relative interiors of the risk adjusted sets of expectations overlap. This condition is necessary if agents are not risk neutral at extreme levels of wealths either positive or negative. It is equivalent to the condition that there does not exist mutually compatible trades, with non negative expected value with respect to any risk adjusted prior, strictly positive for some agent and some prior. It is shown that the more uncertainty averse and the more risk averse, the more likely are efficient allocations and equilibria to exist.
|Date of creation:||Nov 2009|
|Date of revision:|
|Publication status:||Published in Documents de travail du Centre d'Economie de la Sorbonne 2008.39 - ISSN : 1955-611X. 2009|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00281582v2|
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- 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.
- Samet, Dov, 1998.
"Common Priors and Separation of Convex Sets,"
Games and Economic Behavior,
Elsevier, vol. 24(1-2), pages 172-174, 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, 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, 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.
- Billot, A. & Chateauneuf, A. & Gilboa, I. & Tallon, J.-M., 1998.
"Sharing Beliefs: Between Agreeing and Disagreeing,"
Papiers d'Economie MathÃ©matique et Applications
98.30, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing beliefs: between agreeing and disagreeing," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00174553, HAL.
- Itzhak Gilboa & Antoine Billot & Alain Chateauneuf & Jean-Marc Tallon, 2000. "Sharing Beliefs: between Agreeing and Disagreeing," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00753122, HAL.
- 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.
- Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
- 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.
- Lars Tyge Nielsen, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Oxford University Press, vol. 56(3), pages 467-473.
- Atsushi Kajii & Takashi Ui, 2004.
"Agreeable Bets with Multiple Priors,"
KIER Working Papers
581, Kyoto University, Institute of Economic Research.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, 04.
- Shannon, Chris & Strzalecki, Tomasz & Rigotti, Luca, 2008.
"Subjective Beliefs and Ex Ante Trade,"
3637104, Harvard University Department of Economics.
- E. Jouini & W. Schachermayer & N. Touzi, 2008.
"Optimal Risk Sharing For Law Invariant Monetary Utility Functions,"
Wiley Blackwell, vol. 18(2), pages 269-292.
- Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2007. "Optimal Risk Sharing for Law Invariant Monetary Utility Functions," Working Papers halshs-00176606, HAL.
- Rose-Anne Dana, 2004. "Ambiguity, uncertainty aversion and equilibrium welfare," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 569-587, March.
- repec:dau:papers:123456789/5456 is not listed on IDEAS
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004.
"Ambiguity Aversion, Robustness, and the Variational Representation of Preferences,"
Carlo Alberto Notebooks
12, Collegio Carlo Alberto, revised 2006.
- Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
- Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
- repec:dau:papers:123456789/6228 is not listed on IDEAS
- repec:dau:papers:123456789/5393 is not listed on IDEAS
- repec:hal:journl:halshs-00174553 is not listed on IDEAS
- Rose-Anne Dana, 2002. "On Equilibria when Agents Have Multiple Priors," Annals of Operations Research, Springer, vol. 114(1), pages 105-115, August.
- David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172.
- repec:dau:papers:123456789/361 is not listed on IDEAS
- Damir Filipović & Michael Kupper, 2008. "Equilibrium Prices For Monetary Utility Functions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 325-343.
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