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Existence of financial equilibria with restricted participation

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Abstract

We consider a two-date model of a financial exchange economy with finitely many agents having nonordered preferences and portfolio constraints. There is a market for physical commodities at any state today or tomorrow and financial transfers across time and across states are allowed by means of finitely many nominal assets or numeraire assets. We prove a general existence result of equilibria for such a financial exchange economy in which portfolios are defined by linear constraints, extending the framework of linear equality constraints by Balasko et al. (1990) and the existence results in the unconstrained case by Cass (1984, 2006), Werner (1985), Duffie (1987) and Geanakoplos and Polemarchakis (1986). Our main result is a consequence of an auxiliary result, also of interest for itself, in which agents' portofolio constraints are defined by general closed convex sets and the financial structure is assumed to satisfy a "nonredundancy-type" assumption, weaker than the ones in Radner (1972) and Siconolfi (1989).

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Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 09063.

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Length: 25 pages
Date of creation: Oct 2009
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Handle: RePEc:mse:cesdoc:09063

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Keywords: Restricted participation; portofolio constraints; financial exchange economy; equilibrium; existence; arbitrage-free asset prices.;

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References

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  1. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer, vol. 45(1), pages 227-252, October.
  2. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Cahiers de la Maison des Sciences Economiques b04064, Université Panthéon-Sorbonne (Paris 1).
  3. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
  4. Duffie, Darrell & Shafer, Wayne, 1986. "Equilibrium in incomplete markets: II : Generic existence in stochastic economies," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 199-216, June.
  5. Hirsch, M. D. & Magill, M. & Mas-Colell, A., 1990. "A geometric approach to a class of equilibrium existence theorems," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 95-106.
  6. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
  7. Geanakoplos, John & Shafer, Wayne, 1990. "Solving systems of simultaneous equations in economics," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 69-93.
  8. Husseini, S. Y. & Lasry, J. -M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 39-67.
  9. Balasko, Yves & Cass, David & Siconolfi, Paolo, 1990. "The structure of financial equilibrium with exogenous yields : The case of restricted participation," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 195-216.
  10. David Cass, 2006. "Competitive Equilibrium with Incomplete Financial Markets," PIER Working Paper Archive 06-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  11. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
  12. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
  13. Bernard Cornet & Philippe Bich, 2009. "Existence of pseudo-equilibria in a financial economy," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200910, University of Kansas, Department of Economics, revised Dec 2009.
  14. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  15. 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.
  16. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
  17. Laura Angeloni & Bernard Cornet, 2005. "Existence Of Financial Equilibria In A Multiperiod Stochastic Economy," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200506, University of Kansas, Department of Economics, revised Feb 2005.
  18. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
  19. Polemarchakis, H. M. & Siconolfi, P., 1997. "Generic existence of competitive equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 28(3), pages 289-311, October.
  20. repec:hal:cesptp:halshs-00426399 is not listed on IDEAS
  21. Helmut Elsinger & Martin Summer, 2001. "Arbitrage and Optimal Portfolio Choice with Financial Constraints," Working Papers 49, Oesterreichische Nationalbank (Austrian Central Bank).
  22. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
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Citations

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Cited by:
  1. Bernard Cornet & Abhishek Ranjan, 2012. "A remark on arbitrage free prices in multi-period economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00707401, HAL.
  2. Iraola, Miguel & Torres-Martínez, Juan Pablo, 2013. "Liquidity Contractions, Incomplete Financial Participation and the Prevalence of Negative Equity Non-recourse Loans," MPRA Paper 46838, University Library of Munich, Germany.
  3. Bernard Cornet & Abhishek Ranjan, 2012. "A remark on arbitrage free prices in multi-period economy," Documents de travail du Centre d'Economie de la Sorbonne 12035, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  4. 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.
  5. Bernard Cornet & Abhishek Ranjan, 2013. "Existence of equilibria via quasi-equilibria," Documents de travail du Centre d'Economie de la Sorbonne 13020, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  6. 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.
  7. Abdelkrim Seghir & Juan Pablo Torres-Martínez, 2010. "On equilibrium existence with endogenous restricted financial participation," Working Papers wp316, University of Chile, Department of Economics.
  8. Jean-Marc Bonnisseau & Achis Chery, 2013. "On the equivalence of financial structures with short-term assets," Documents de travail du Centre d'Economie de la Sorbonne 13079, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  9. 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.
  10. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer, vol. 45(1), pages 227-252, October.
  11. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
  12. 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.
  13. Bernard Cornet & Abhishek Ranjan, 2013. "Existence of equilibria via quasi-equilibria," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801399, HAL.
  14. Cea-Echenique, Sebastián & Torres-Martínez, Juan Pablo, 2014. "General Equilibrium with Endogenous Trading Constraints," MPRA Paper 55359, University Library of Munich, Germany.
  15. Gori, Michele & Pireddu, Marina & Villanacci, Antonio, 2013. "Regularity and Pareto improving on financial equilibria with price-dependent borrowing restrictions," Research in Economics, Elsevier, vol. 67(1), pages 100-110.
  16. Jean-Marc Bonnisseau & Achis Chery, 2013. "On the equivalence of financial structures with short-term assets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00917644, HAL.
  17. Michele Gori & Marina Pireddu & Antonio Villanacci, 2010. "Regularity and Pareto Improving on financial equilibria with endogenous borrowing restrictions," Working Papers - Mathematical Economics 2010-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa, revised Aug 2012.
  18. 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.
  19. 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.

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