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Existence of financial equilibria with restricted participation

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  • Zaier Aouani

    ()
    (International School of Economics at TSU, Tbilisi, Republic of Georgia)

  • Bernard Cornet

    ()
    (University of Kansas, Lawrence, Kansas, United States and University of Paris 1 Pantheon-Sorbonne, Paris, France)

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' portfolio 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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Bibliographic Info

Paper provided by International School of Economics at TSU, Tbilisi, Republic of Georgia in its series Working Papers with number 001-09.

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Length: 30 pages
Date of creation: Sep 2009
Date of revision:
Handle: RePEc:tbs:wpaper:09-001

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

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  1. Bernard Cornet & Ramu Gopalan, 2009. "Arbitrage and Equilibrium with Portfolio Constraints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00441873, HAL.
  2. Helmut Elsinger & Martin Summer, 2001. "Arbitrage and Optimal Portfolio Choice with Financial Constraints," Working Papers 49, Oesterreichische Nationalbank (Austrian Central Bank).
  3. 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.
  4. 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.
  5. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
  6. 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.
  7. 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.
  8. Geanakoplos, John & Shafer, Wayne, 1990. "Solving systems of simultaneous equations in economics," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 69-93.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  14. 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.
  15. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
  16. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Cahiers de la Maison des Sciences Economiques b04064, Université Panthéon-Sorbonne (Paris 1).
  17. 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.
  18. 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.
  19. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
  20. 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.
  21. 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.
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