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Incomplete-Market Equilibria Solved Recursively on an Event Tree

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Author Info
Bernard Dumas
Andrew Lyasoff
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 National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14629.

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Date of creation: Dec 2008
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Handle: RePEc:nbr:nberwo:14629

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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.
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  4. 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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  5. Fatih Guvenen, 2009. "A parsimonious macroeconomic model for asset pricing," Staff Report 434, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  6. 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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  7. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July. [Downloadable!] (restricted)
  8. 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)
  9. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543, December.
  10. Dirk Krueger & Hanno Lustig, 2006. "When is Market Incompleteness Irrelevant for the Price of Aggregate Risk (and when is it not)?," NBER Working Papers 12634, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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