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Arbitrage and equilibrium with portfolio constraints

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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 (Non-linear Dynamics in Economics and Social Sciences, 1989). Using an approach that dates back to Cass (CARESS Working Paper, 1984; J Math Econ 42:384–405, 2006) in the unconstrained case, we seek to isolate arbitrage-free asset prices that are also 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 deduces 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 (Working Paper, University of Paris 1, 2005).

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References

  • Angeloni L., Cornet B.: Existence of financial equilibria in a multi-period stochastic economy. Adv Math Econ 8, 1–31 (2006)

    Article  Google Scholar 

  • Aouani, Z., Cornet, B.: Existence of financial equilibria with restricted participation. J Math Econ (2009, forthcoming)

  • Balasko Y., Cass D.: The structure of financial equilibrium with exogenous yields: the case of incomplete markets. Econometrica 57, 135–162 (1989)

    Article  Google Scholar 

  • Bich P., Cornet B.: Fixed-point-like theorems on subspaces. Fixed Point Theory Appl 3, 159–171 (2004)

    Article  Google Scholar 

  • Bich, P., Cornet, B.: Existence of pseudo-equilibria in a financial economy. Fixed Point Theory Appl (2009, forthcoming)

  • Carosi, L., Gori, M., Villanacci, A.: Endogenous restricted participation in general financial equilibrium. J Math Econ (2009, forthcoming)

  • Cass, D.: Competitive equilibrium with incomplete financial markets. CARESS Working Paper, University of Pennsylvania (1984)

  • Cass D.: Sunspots and incomplete financial markets: the general case. Econ Theory 2, 341–358 (1992)

    Article  Google Scholar 

  • Cass D.: Competitive equilibrium with incomplete financial markets. J Math Econ 42, 384–405 (2006)

    Article  Google Scholar 

  • Cass D., Siconolfi P., Villanacci A.: Generic regularity of competitive equilibria with restricted participation. J Math Econ 36, 61–76 (2001)

    Article  Google Scholar 

  • Cornet B., De Boisdeffre L.: Arbitrage and price revelation with asymmetric information and incomplete markets. J Math Econ 38, 393–410 (2002)

    Article  Google Scholar 

  • Cornet B., De Boisdeffre L.: Elimination of arbitrage states in asymmetric information models. Econ Theory 38, 287–293 (2009)

    Article  Google Scholar 

  • Cornet, B., Gopalan, R.: Restricted participation and arbitrage in a multiperiod model. Working Paper, University of Kansas (2006)

  • Debreu G.: Theory of Value. Cowles Foundation Monograph 17. Yale University Press, New Haven/London (1959)

    Google Scholar 

  • Dubey P., Geanakoplos J.: Determinacy with nominal assets and outside money. Econ Theory 27, 79–106 (2006)

    Article  Google Scholar 

  • Duffie D.: Stochastic equilibria with incomplete financial markets. J Econ Theory 41, 405–416 (1987)

    Article  Google Scholar 

  • Duffie D., Shafer W.: Equilibrium in incomplete markets. I. A basic model of generic existence. J Math Econ 14, 285–300 (1985)

    Article  Google Scholar 

  • Duffie D., Shafer W.: Equilibrium in incomplete markets. II. Generic existence in stochastic economies. J Math Econ 15, 199–216 (1986)

    Article  Google Scholar 

  • Elsinger, H., Summer, M.: Arbitrage and optimal portfolio choice with financial constraints. Working Paper, Austrian Central Bank 49 (2001)

  • Florig M., Meddeb M.: Slack in incomplete markets with nominal assets: a symmetric proof. J Math Econ 43, 640–655 (2007)

    Article  Google Scholar 

  • Gale D., Mas-Colell A.: An equilibrium existence theorem for a general model without ordered preferences. J Math Econ 2, 9–15 (1975)

    Article  Google Scholar 

  • Geanakoplos J., Mas-Colell A.: Real indeterminacy with financial assets. J Econ Theory 47, 22–38 (1989)

    Article  Google Scholar 

  • Geanakoplos J., Polemarchakis H.: Existence, regularity, and constrained suboptimality of competitive allocations when the asset market is incomplete. In: Heller, W., Starr, R., Starrett, D. (eds) Uncertainty, information and communication: Essays in Honor of Kenneth Arrow, vol. 3, pp. 65–95. Cambridge University Press, Cambridge (1986)

    Google Scholar 

  • Geanakopolos J., Shafer W.: Solving systems of simultaneous equations in economics. J Math Econ 19, 69–93 (1990)

    Article  Google Scholar 

  • Gottardi P., Hens T.: The survival assumption and existence of competitive equilibria when asset markets are incomplete. J Econ Theory 71, 313–323 (1996)

    Article  Google Scholar 

  • Hart O.: On the optimality of equilibrium when the market structure is incomplete. J Econ Theory 11, 418–443 (1975)

    Article  Google Scholar 

  • Hens T., Herings J.-J., Predtetchinskii A.: Limits to arbitrage when market participation is restricted. J Math Econ 42, 556–564 (2006)

    Article  Google Scholar 

  • Hirsch M., Magill M., Mas-Colell A.: A geometric approach to a class of equilibrium existence theorems. J Econ 19, 95–106 (1990)

    Google Scholar 

  • Husseini S., Lasry J., Magill M.: Existence of equilibrium with incomplete markets. J Math Econ 19, 39–67 (1990)

    Article  Google Scholar 

  • Koutsougeras L., Papadoupoulos K.: Arbitrage and equilibrium in strategic security markets. Econ Theory 23, 553–568 (2004)

    Article  Google Scholar 

  • Magill M., Quinzii M.: Theory of Incomplete Markets. MIT Press, Cambridge, MA (1996)

    Google Scholar 

  • Magill M., Shafer W.: Incomplete markets. In: Hildenbrand, W., Sonnenschein, H. (eds) Handbook of Mathematical Economics, vol. 4, pp. 1523–1614. Elsevier, Amsterdam (1991)

    Google Scholar 

  • Martins-da-Rocha, V. F., Triki, L.: Equilibria in exchange economies with financial constraints: beyond the Cass trick. Working Paper, University of Paris 1 (2005)

  • Polemarchakis H.J., Siconolfi P.: Asset markets and the information revealed by prices. Econ Theory 3, 645–661 (1993)

    Article  Google Scholar 

  • Radner R.: Existence of equilibrium of plans, prices, and price expectations in a sequence of markets. Econometrica 40, 289–303 (1972)

    Article  Google Scholar 

  • Radner R., Rothschild M.: On the allocation of effort. J Econ Theory 10, 358–376 (1975)

    Article  Google Scholar 

  • Rockafellar R.T.: Convex Analysis. Princeton University Press, Princeton (1970)

    Google Scholar 

  • Seghir, A., Triki, L., Kanellopoulou, S.: On the survival and irreducibility assumptions for financial markets with nominal assets. Working Paper, University of Paris 1 (2004)

  • Siconolfi P.: Equilibrium with asymmetric constraints on portfolio holdings and incomplete financial markets. In: Galeotti, L., Geronazzo, L., Gori, F. (eds) Nonlinear dynamics in economics and social sciences, pp. 271–292. Societa Pitagora, Bologna (1989)

    Google Scholar 

  • Villanacci A., Carosi L., Beneveri P., Battinelli A.: Differential Topology and General Equilibrium with Incomplete Markets. Kluwer Academic Publishers, Dordrecht (2002)

    Google Scholar 

  • Werner J.: Equilibrium in economies with incomplete financial markets. J Econ Theory 36, 110–119 (1985)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. University of Kansas, Lawrence, KS, USA

    Bernard Cornet

  2. University of Paris 1, Paris, France

    Bernard Cornet & Ramu Gopalan

Authors
  1. Bernard Cornet
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  2. Ramu Gopalan
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Correspondence to Bernard Cornet.

Additional information

We wish to thank Philippe Bich, Jean-Marc Bonnisseau, Michael Magill, Martine Quinzii, and Nicholas Yannelis for discussions and valuable comments.

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Cornet, B., Gopalan, R. Arbitrage and equilibrium with portfolio constraints. Econ Theory 45, 227–252 (2010). https://doi.org/10.1007/s00199-009-0506-5

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