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Arbitrage and equilibrium with portfolio constraints

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  • Bernard Cornet

    ()

  • Ramu Gopalan

    ()

Abstract

We consider a multiperiod financial exchange economy with nominal assets and restricted participation, where each agent's portfolio choice is restricted to a closed, convex set containing zero, as in Siconolfi (1989). Using an approach that dates back to Cass (1984, 2006) in the unconstrained case, we seek to isolate arbitrage-free asset prices that are aloso quasi-equilibrium or equilibrium asset prices. In the presence of such portfolio restrictions, we need to confine our attention to aggregate arbitrage-free asset prices, i.e., for which there is no arbitrage in the space of marketed portfolios. Our main result states that such asset prices are quasi-equilibrium prices under standard assumptions and then deduce that they are equilibrium prices under a suitable condition on the accessibility of payoffs by agents, i.e., every payoff that is attainable in the aggregate can be marketed through some agent's portfolio set. This latter result extends previous work by Martins-da-Rocha and Triki (2005).

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 45 (2010)
Issue (Month): 1 (October)
Pages: 227-252

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Handle: RePEc:spr:joecth:v:45:y:2010:i:1:p:227-252

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Related research

Keywords: Stochastic financial exchange economies; Incomplete markets; Financial equilibrium; Constrained portfolios; Multiperiod models; Arbitrage-free asset prices; C62; D52; D53; G11; G12;

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References

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  1. Zaier Aouani & Bernard Cornet, 2009. "Existence of financial equilibria with restricted participation," Documents de travail du Centre d'Economie de la Sorbonne 09063, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. repec:hal:cesptp:halshs-00426399 is not listed on IDEAS
  3. Pradeep Dubey & John Geanakoplos, 2006. "Determinacy with nominal assets and outside money," Economic Theory, Springer, vol. 27(1), pages 79-106, 01.
  4. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614 Elsevier.
  5. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Cahiers de la Maison des Sciences Economiques b04064, Université Panthéon-Sorbonne (Paris 1).
  6. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
  7. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer, vol. 38(2), pages 287-293, February.
  8. Gottardi, Piero & Hens, Thorsten, 1996. "The Survival Assumption and Existence of Competitive Equilibria When Asset Markets are Incomplete," Journal of Economic Theory, Elsevier, vol. 71(2), pages 313-323, November.
  9. Hens,Thorsten & Herings,P. Jean-Jacques & Predtetchinskii,Arkadi, 2003. "Limits to Arbitrage when Market Participation Is Restricted," Research Memorandum 061, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  10. Carosi, Laura & Gori, Michele & Villanacci, Antonio, 2009. "Endogenous restricted participation in general financial equilibrium," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 787-806, December.
  11. John Geanakoplos & Andreu Mas-Colell, 1985. "Real Indeterminacy with Financial Assets," Cowles Foundation Discussion Papers 770R, Cowles Foundation for Research in Economics, Yale University, revised Oct 1985.
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  15. Philippe Bich & Bernard Cornet, 2009. "Existence of pseudo-equilibria in a financial economy," Documents de travail du Centre d'Economie de la Sorbonne 09060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
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  17. Abdelkrim Seghir & Leila Triki & Stella Kanellopoulou, 2004. "On the survival and irreducibility assumptions for financial markets with nominal assets," Cahiers de la Maison des Sciences Economiques b04008, Université Panthéon-Sorbonne (Paris 1).
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  28. Polemarchakis, H M & Siconolfi, P, 1993. "Asset Markets and the Information Revealed by Prices," Economic Theory, Springer, vol. 3(4), pages 645-61, October.
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  30. Cass, David & Siconolfi, Paolo & Villanacci, Antonio, 2001. "Generic regularity of competitive equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 61-76, September.
  31. Florig, Michael & Meddeb, Moncef, 2007. "Slack in incomplete markets with nominal assets: A symmetric proof," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 640-655, June.
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Citations

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Cited by:
  1. Zaier Aouani & Bernard Cornet, 2009. "Existence of financial equilibria with restricted participation," Documents de travail du Centre d'Economie de la Sorbonne 09063, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Jean-Marc Bonnisseau & Achis Chery, 2013. "Stability of marketable payoffs with long-term assets," Documents de travail du Centre d'Economie de la Sorbonne 13078, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
  4. Jean-Marc Bonnisseau & Achis Chery, 2013. "Sensitivity of marketable payoffs with long-term assets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00821094, HAL.
  5. repec:hal:journl:halshs-00659183 is not listed on IDEAS
  6. Miguel A. Iraola & Juan Pablo Torres-Martinez, 2013. "Liquidity Contractions, Incomplete Financial Participation and the Prevalence of Negative Equity Non-Recourse Loans," Working Papers 2013-08, University of Miami, Department of Economics.
  7. Pérez Fernández, Víctor & Torres-Martínez, Juan Pablo, 2012. "Incomplete financial participation: exclusive markets, investment clubs and credit risk," MPRA Paper 36624, University Library of Munich, Germany.
  8. Jean-Marc Bonnisseau & Achis Chery, 2013. "Tackling the instability of growth: A Kaleckian model with autonomous demand expenditures," Documents de travail du Centre d'Economie de la Sorbonne 13029, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  9. Jean-Marc Bonnisseau & Achis Chery, 2013. "Stability of marketable payoffs with long-term assets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00917638, HAL.
  10. Cea-Echenique, Sebastián & Torres-Martínez, Juan Pablo, 2014. "General Equilibrium with Endogenous Trading Constraints," MPRA Paper 55359, University Library of Munich, Germany.
  11. Abdelkrim Seghir & Juan Pablo Torres-Martínez, 2010. "On equilibrium existence with endogenous restricted financial participation," Working Papers wp316, University of Chile, Department of Economics.
  12. Sebastián Cea-Echenique & Carlos Hervés-Beloso & Juan Pablo Torres-Martínez, 2012. "Endogenous Information: The Role of Sequential Trade and Financial Participation," Working Papers wp361, University of Chile, Department of Economics.

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