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Incomplete-Market Equilibria Solved Recursively on an Event Tree

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Author Info
Dumas, Bernard J
Lyasoff, Andrew
Abstract

We develop a method that allows one to compute incomplete-market equilibria routinely for Markovian equilibria (when they exist). The main difficulty to be overcome arises from the set of state variables. There are, of course, exogenous state variables driving the economy but, in an incomplete market, there are also endogenous state variables, which introduce path dependence. We write on an event tree the system of all first-order conditions of all times and states and solve recursively for state prices, which are dual variables. We illustrate this “dual” method and show its many practical advantages by means of several examples.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7138.

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Date of creation: Jan 2009
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Handle: RePEc:cpr:ceprdp:7138

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Related research
Keywords: computation; financial-market equilibrium; incomplete market; recursive methods;

Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C68 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - 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
D91 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Consumer Choice; Life Cycle Models and Saving
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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  1. Felix Kubler & Karl Schmedders, 2003. "Stationary Equilibria in Asset-Pricing Models with Incomplete Markets and Collateral," Econometrica, Econometric Society, vol. 71(6), pages 1767-1793, November. [Downloadable!] (restricted)
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  2. Husseini, S. Y. & Lasry, J. -M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 39-67. [Downloadable!] (restricted)
  3. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Infinite Dimensional Case," Research Program in Finance Working Papers RPF-191, University of California at Berkeley.
    Other versions:
  4. Hirsch, M. D. & Magill, M. & Mas-Colell, A., 1990. "A geometric approach to a class of equilibrium existence theorems," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 95-106. [Downloadable!] (restricted)
  5. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October. [Downloadable!] (restricted)
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  6. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Fatih Guvenen, 2009. "A parsimonious macroeconomic model for asset pricing," Staff Report 434, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  9. Krebs, Tom, 2004. "Non-existence of recursive equilibria on compact state spaces when markets are incomplete," Journal of Economic Theory, Elsevier, vol. 115(1), pages 134-150, March. [Downloadable!] (restricted)
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  10. Fatih Guvenen & Burhanettin Kuruscu, 2006. "Does Market Incompleteness Matter for Asset Prices?," Journal of the European Economic Association, MIT Press, vol. 4(2-3), pages 484-492, 04-05. [Downloadable!] (restricted)
  11. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543.
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