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Computing Equilibria in Finance Economies

Author

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  • P.J.J. Herings

    (University of Maastricht)

  • F. Kubler

    (Stanford University)

Abstract

The general equilibrium model with incomplete asset markets provides a unified framework for many problems in finance and macroeconomics. In its simplest version with only two time periods and a single physical commodity the model is ideally suited for the study of problems in cross sectional asset pricing and portfolio theory. In this paper we develop a homotopy algorithm to approximate equilibria in these ''finance economies''. Since the algorithm is tailor made for finance economies, the number of nonlinear equations that has to be solved for, and therefore the computing time,is an order of magnitude smaller than that of existing general purpose algorithms.The algorithm is shown to be generically convergent. We implement the algorithm using HOMPACK. To illustrate its performance, we present various numerical examples and report running times.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • P.J.J. Herings & F. Kubler, 2001. "Computing Equilibria in Finance Economies," GE, Growth, Math methods 0205003, EconWPA.
  • Handle: RePEc:wpa:wuwpge:0205003
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    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, April.
    2. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    3. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, March.
    4. 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.
    5. 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.
    6. 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.
    7. Herings, P.J.J. & Kubler, F., 1999. "The Robustness of the CAPM - A Computational Approach," Discussion Paper 1999-54, Tilburg University, Center for Economic Research.
    8. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
    9. Doup, T.M. & van der Laan, G. & Talman, A.J.J., 1984. "The (2n+1-2)-ray algorithm : A new simplicial algorithm to compute economic equilibria," Research Memorandum FEW 151, Tilburg University, School of Economics and Management.
    10. 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.
    11. 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.
    12. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
    13. Herings,O. Jean-Jacques & Kubler,Felix, 2000. "The Robustness of CAPM-A Computational Approach," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. 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.
    15. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    16. Hens,Thorsten, 1991. "Structure of general equilibrium models with incomplete markets and a single consumption good," Discussion Paper Serie A 353, University of Bonn, Germany.
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    Citations

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    Cited by:

    1. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    2. P. Herings & Felix Kubler, 2007. "Approximate CAPM When Preferences are CRRA," Computational Economics, Springer;Society for Computational Economics, vol. 29(1), pages 13-31, February.
    3. Herings, P.J.J. & Kubler, F., 1999. "The Robustness of the CAPM - A Computational Approach," Discussion Paper 1999-54, Tilburg University, Center for Economic Research.
    4. Esteban-Bravo, Mercedes, 2004. "An interior point algorithm for computing equilibria in economies with incomplete asset markets," DEE - Working Papers. Business Economics. WB wb046023, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    5. Jacco Thijssen, 2008. "A computational study on general equilibrium pricing of derivative securities," Annals of Finance, Springer, vol. 4(4), pages 505-523, October.
    6. Talman, A.J.J. & Thijssen, J.J.J., 2006. "Existence of equilibrium and price adjustments in a finance economy with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 255-268, June.
    7. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    Computational methods; asset pricing; general equilibrium; incomplete markets.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • 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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