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Computing Equilibria in Finance Economies

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Author Info

  • 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.)

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File URL: http://128.118.178.162/eps/ge/papers/0205/0205003.pdf
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Bibliographic Info

Paper provided by EconWPA in its series GE, Growth, Math methods with number 0205003.

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Length: 16 pages
Date of creation: 31 Oct 2001
Date of revision:
Handle: RePEc:wpa:wuwpge:0205003

Note: Type of Document - pdf.format; pages: 16
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Web page: http://128.118.178.162

Related research

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

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References

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  1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  2. 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.
  3. 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.
  4. Mas-Colell,Andreu, 1985. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521265140.
  5. P. Jean-Jacques Herings & Felix Kubler, 2000. "The Robustness of the CAPM-A Computational Approach," Econometric Society World Congress 2000 Contributed Papers 0400, Econometric Society.
  6. Herings, P.J.J., 1994. "A globally and universally stable price adjustment process," Discussion Paper 1994-52, Tilburg University, Center for Economic Research.
  7. Doup, T.M. & Laan, G. van der & Talman, A.J.J., 1984. "The (2n+1-2)-ray algorithm: A new simplicial algorithm to compute economic equilibria," Research Memorandum 151, Tilburg University, Faculty of Economics and Business Administration.
  8. 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.
  9. 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.
  10. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, 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. 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.
  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).
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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. Jacco Thijssen, 2008. "A computational study on general equilibrium pricing of derivative securities," Annals of Finance, Springer, vol. 4(4), pages 505-523, October.
  3. P. Herings & Felix Kubler, 2007. "Approximate CAPM When Preferences are CRRA," Computational Economics, Society for Computational Economics, vol. 29(1), pages 13-31, February.
  4. Mercedes Esteban-Bravo, 2004. "An Interior Point Algorithm For Computing Equilibria In Economies With Incomplete Asset Markets," Business Economics Working Papers wb046023, Universidad Carlos III, Departamento de Economía de la Empresa.
  5. Talman, A.J.J. & Thijssen, J.J.J., 2003. "Existence of Equilibrium and Price Adjustments in a Finance Economy with Incomplete Markets," Discussion Paper 2003-79, Tilburg University, Center for Economic Research.
  6. P. Jean-Jacques Herings & Felix Kubler, 2000. "The Robustness of the CAPM-A Computational Approach," Econometric Society World Congress 2000 Contributed Papers 0400, Econometric Society.

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