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Computing Equilibria in Finance Economies with Incomplete Markets and Transaction Costs

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  • P. Jean-Jacques Herings
  • Karl Schmedders

Abstract

Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents’ asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria. Copyright Springer-Verlag Berlin/Heidelberg 2006
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  • P. Jean-Jacques Herings & Karl Schmedders, 2001. "Computing Equilibria in Finance Economies with Incomplete Markets and Transaction Costs," Discussion Papers 1318, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1318
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    References listed on IDEAS

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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, March.
    2. Herings P. Jean-Jacques & Peeters R., 1999. "A Differentiable Homotopy to Compute Nash Equilibria of n-Person Games," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    4. Aiyagari, S. Rao & Gertler, Mark, 1991. "Asset returns with transactions costs and uninsured individual risk," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 311-331, June.
    5. Arrow, Kenneth J. & Hahn, Frank, 1999. "Notes on Sequence Economies, Transaction Costs, and Uncertainty," Journal of Economic Theory, Elsevier, vol. 86(2), pages 203-218, June.
    6. Demarzo, Peter M. & Eaves, B. Curtis, 1996. "Computing equilibria of GEI by relocalization on a Grassmann manifold," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 479-497.
    7. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
    8. Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
    9. Elul, Ronel, 1997. "Financial innovation, precautionary saving and the risk-free rate," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 113-131, February.
    10. Pradeep Dubey & John Geanakoplos & Martin Shubik, 1988. "Default and Efficiency in a General Equilibrium Model with Incomplete Markets," Cowles Foundation Discussion Papers 879R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1989.
    11. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters,in: Theory Of Valuation, chapter 7, pages 207-227 World Scientific Publishing Co. Pte. Ltd..
    12. 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.
    13. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-487, June.
    14. Schmedders, Karl, 1998. "Computing equilibria in the general equilibrium model with incomplete asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1375-1401, August.
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    16. Aiyagari, S. Rao & Gertler, Mark, 1991. "Asset returns with transactions costs and uninsured individual risk," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 311-331, June.
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    Cited by:

    1. V. Filipe MARTINS-DA-ROCHA & YIANNIS VAILAKIS, 2008. "Endogenous Transaction Costs," Discussion Papers 0810, Exeter University, Department of Economics.
    2. 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.
    3. 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.
    4. Buss, Adrian & Dumas, Bernard J, 2013. "Financial-market Equilibrium with Friction," CEPR Discussion Papers 9524, C.E.P.R. Discussion Papers.
    5. Michele Gori & Marina Pireddu & Antonio Villanacci, 2010. "Regularity and Pareto Improving on financial equilibria with endogenous borrowing restrictions," Working Papers - Mathematical Economics 2010-08, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa, revised Aug 2012.
    6. V. Martins-da-Rocha & Yiannis Vailakis, 2010. "Financial markets with endogenous transaction costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 65-97, October.
    7. Marko Backovic & Zoran Popovic, 2012. "The Analysis Of Model Of General Economic Equilibrium And Financial Instability Of Economic System," Montenegrin Journal of Economics, Economic Laboratory for Transition Research (ELIT), vol. 8(1), pages 63-85.

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