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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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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/mic/papers/0503/0503013.pdf
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    References listed on IDEAS

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

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    Cited by:

    1. 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.
    2. 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.
    3. Cea-Echenique, Sebastián & Torres-Martínez, Juan Pablo, 2014. "General Equilibrium with Endogenous Trading Constraints," MPRA Paper 55359, University Library of Munich, Germany.
    4. Cea-Echenique, Sebastián & Torres-Martínez, Juan Pablo, 2016. "Credit segmentation in general equilibrium," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 19-27.
    5. Bernard Cornet & Abhishek Ranjan, 2013. "Equilibria in a multi-period economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801402, HAL.

    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.;

    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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