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Arbitrage and Equilibrium with Portfolio Constraints

Author

Listed:
  • Bernard Cornet

    (Department of Economics, The University of Kansas)

  • Ramu Gopalan

    (Washington and Jefferson College)

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 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 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).

Suggested Citation

  • Bernard Cornet & Ramu Gopalan, 2009. "Arbitrage and Equilibrium with Portfolio Constraints," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200911, University of Kansas, Department of Economics, revised Dec 2009.
    • Handle: RePEc:kan:wpaper:200911
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    File URL: http://www2.ku.edu/~kuwpaper/2009Papers/200911.pdf
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    References listed on IDEAS

    as
    1. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    2. 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.
    3. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    4. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    5. Bernard Cornet & Lionel Boisdeffre, 2009. "Elimination of arbitrage states in asymmetric information models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 287-293, February.
    6. Leonidas Koutsougeras & Konstantinos Papadopoulos, 2004. "Arbitrage and equilibrium in strategic security markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 553-568, March.
    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. 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.
    9. 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.
    10. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Post-Print halshs-03330770, HAL.
    11. Balasko, Yves & Cass, David, 1989. "The Structure of Financial Equilibrium with Exogenous Yields: The Case of Incomplete Markets," Econometrica, Econometric Society, vol. 57(1), pages 135-162, January.
    12. Geanakoplos, J. & Polemarchakis, H., 1985. "Existence,regularity, and constrained suboptimality of competitive allocations when the asset market is incomplete," LIDAM Discussion Papers CORE 1985037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. Philippe Bich & Bernard Cornet, 2009. "Existence of pseudo-equilibria in a financial economy," Post-Print halshs-00426399, HAL.
    14. 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.
    15. 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.
    16. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
    17. Pradeep Dubey & John Geanakoplos, 2006. "Determinacy with nominal assets and outside money," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(1), pages 79-106, January.
    18. Radner, Roy & Rothschild, Michael, 1975. "On the allocation of effort," Journal of Economic Theory, Elsevier, vol. 10(3), pages 358-376, June.
    19. 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).
    20. Duffie, Darrell & Sonnenschein, Hugo, 1989. "Arrow and General Equilibrium Theory," Journal of Economic Literature, American Economic Association, vol. 27(2), pages 565-598, June.
    21. 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.
    22. Hens, Thorsten & Jean-Jacques Herings, P. & Predtetchinskii, Arkadi, 2006. "Limits to arbitrage when market participation is restricted," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 556-564, August.
    23. Helmut Elsinger & Martin Summer, 2001. "Arbitrage and Optimal Portfolio Choice with Financial Constraints," Working Papers 49, Oesterreichische Nationalbank (Austrian Central Bank).
    24. 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.
    25. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Post-Print halshs-01394846, HAL.
    26. V.F. Martins-da-Rocha & L. Triki, 2005. "Equilibria in exchange economies with financial constraints: Beyond the Cass Trick," Microeconomics 0503013, University Library of Munich, Germany.
    27. 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.
    28. Geanakoplos, John & Mas-Colell, Andreu, 1989. "Real indeterminacy with financial assets," Journal of Economic Theory, Elsevier, vol. 47(1), pages 22-38, February.
    29. 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.
    30. Polemarchakis, H M & Siconolfi, P, 1993. "Asset Markets and the Information Revealed by Prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(4), pages 645-661, October.
    31. 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.
    32. Cass, David, 1992. "Sunspots and Incomplete Financial Markets: The General Case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(3), pages 341-358, July.
    33. 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.
    34. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
    35. repec:onb:oenbwp:y::i:49:b:1 is not listed on IDEAS
    36. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
    37. 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.
    38. Cornet, Bernard & De Boisdeffre, Lionel, 2002. "Arbitrage and price revelation with asymmetric information and incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 393-410, December.
    39. W. Hildenbrand & H. Sonnenschein (ed.), 1991. "Handbook of Mathematical Economics," Handbook of Mathematical Economics, Elsevier, edition 1, volume 4, number 4.
    40. Philippe Bich & Bernard Cornet, 2004. "Fixed-point-like theorems on subspaces," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03330770, HAL.
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    More about this item

    Keywords

    Stochastic Financial exchange economies; Incomplete markets; Financial equilibrium; Constrained portfolios; Multiperiod models; Arbitrage-free asset prices;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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