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Equilibria in exchange economies with financial constraints: Beyond the Cass Trick

Author

Listed:
  • V.F. Martins-da-Rocha

    (CEREMADE)

  • L. Triki

    (CERMSEM)

Abstract

We consider an exchange economy under incomplete financial markets with purely financial securities and finitely many agents. When portfolios are not constrained, Cass (1984), Duffie (1987) and Florenzano--Gourdel (1992) proved that arbitrage-free security prices fully characterize equilibrium security prices. This result is based on a trick initiated by Cass (1984) in which one unconstrained agent behaves as if he were in complete markets. This approach is unsatisfactory since it is asymmetric and no more valid when every agent is subject to frictions. We propose a new and symmetric approach to prove that arbitrage-free security prices still fully characterize equilibrium security prices in the more realistic situation where the financial market is constrained by convex restrictions, provided that financial markets are collectively frictionless.

Suggested Citation

  • 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.
    • Handle: RePEc:wpa:wuwpmi:0503013
    Note: Type of Document - pdf; pages: 18
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    References listed on IDEAS

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    1. 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.
    2. Monique Florenzano, 1999. "General equilibrium of financial markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00085543, HAL.
    3. Monique Florenzano, 2007. "General equilibrium," Post-Print halshs-00250167, HAL.
    4. Lawrence M. Benveniste & Juan Ketterer, 1992. "Arbitrage Opportunities in Financial Markets are not Inconsistent with Competitive Equilibrium," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 4, pages 45-54, Palgrave Macmillan.
    5. Duffie, Darrell, 1987. "Stochastic equilibria with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 41(2), pages 405-416, April.
    6. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-1467, November.
    7. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
    8. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
    9. Rahi, Rohit, 1995. "Partially revealing rational expectations equilibria with nominal assets," Journal of Mathematical Economics, Elsevier, vol. 24(2), pages 137-146.
    10. Florenzano, Monique & Gourdel, Pascal, 1994. "T-period economies with incomplete markets," Economics Letters, Elsevier, vol. 44(1-2), pages 91-97.
    11. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
    12. 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.
    13. Helmut Elsinger & Martin Summer, 2001. "Arbitrage and Optimal Portfolio Choice with Financial Constraints," Working Papers 49, Oesterreichische Nationalbank (Austrian Central Bank).
    14. repec:dau:papers:123456789/6894 is not listed on IDEAS
    15. 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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    Cited by:

    1. Bernard Cornet & Abhishek Ranjan, 2013. "Equilibria in a multi-period economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801402, HAL.
    2. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    3. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 227-252, October.
    4. 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.
    5. Sebastián Cea-Echenique & Juan Pablo Torres-Martínez, 2018. "General equilibrium with endogenous trading constraints," PLOS ONE, Public Library of Science, vol. 13(9), pages 1-10, September.
    6. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    7. Cea-Echenique, Sebastián & Torres-Martínez, Juan Pablo, 2016. "Credit segmentation in general equilibrium," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 19-27.

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    More about this item

    Keywords

    Exchange economies; incomplete financial markets; purely financial securities; nominal assets; constrained portfolios; collectively frictionless financial markets; equilibrium security prices; arbitrage-free security 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
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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