IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/7138.html
   My bibliography  Save this paper

Incomplete-Market Equilibria Solved Recursively on an Event Tree

Author

Listed:
  • Dumas, Bernard
  • 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.

Suggested Citation

  • Dumas, Bernard & Lyasoff, Andrew, 2009. "Incomplete-Market Equilibria Solved Recursively on an Event Tree," CEPR Discussion Papers 7138, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:7138
    as

    Download full text from publisher

    File URL: https://cepr.org/publications/DP7138
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Basak, Suleyman & Cuoco, Domenico, 1998. "An Equilibrium Model with Restricted Stock Market Participation," The Review of Financial Studies, Society for Financial Studies, vol. 11(2), pages 309-341.
    2. Krueger, Dirk & Lustig, Hanno, 2010. "When is market incompleteness irrelevant for the price of aggregate risk (and when is it not)?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 1-41, January.
    3. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    4. Lucas, Deborah J., 1994. "Asset pricing with undiversifiable income risk and short sales constraints: Deepening the equity premium puzzle," Journal of Monetary Economics, Elsevier, vol. 34(3), pages 325-341, December.
    5. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(2), pages 284-306, April.
    6. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    7. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-872.
    8. 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.
    9. Duffie, Darrell & Shafer, Wayne, 1986. "Equilibrium in incomplete markets: II : Generic existence in stochastic economies," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 199-216, June.
    10. 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.
    11. Jouini, Elyes & Kallal, Hedi, 2001. "Efficient Trading Strategies in the Presence of Market Frictions," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 343-369.
    12. Fatih Guvenen, 2009. "A Parsimonious Macroeconomic Model for Asset Pricing," Econometrica, Econometric Society, vol. 77(6), pages 1711-1750, November.
    13. 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.
    14. 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.
    15. Michael Magill & Martine Quinzii, 2002. "Theory of Incomplete Markets, Volume 1," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262632543, April.
    16. 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.
    17. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    18. Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
    19. repec:dau:papers:123456789/4721 is not listed on IDEAS
    20. Francisco Gomes & Alexander Michaelides, 2008. "Asset Pricing with Limited Risk Sharing and Heterogeneous Agents," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 415-448, January.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bernard Dumas & Pascal Maenhout, 2002. "A Central-Planning Approach to Dynamic Incomplete-Market Equilibrium," Levine's Working Paper Archive 391749000000000523, David K. Levine.
    2. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    3. Sydney Ludvigson & Stijn Van Nieuwerburgh & Jack Favilukis, 2012. "Foreign Ownership of U.S. Safe Assets: Good or Bad?," 2012 Meeting Papers 297, Society for Economic Dynamics.
    4. Bernard Cornet & Ramu Gopalan, 2010. "Arbitrage and equilibrium with portfolio constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 227-252, October.
    5. Philippe Bich & Bernard Cornet, 2009. "Existence of pseudo-equilibria in a financial economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00426399, HAL.
    6. Favilukis, Jack, 2013. "Inequality, stock market participation, and the equity premium," Journal of Financial Economics, Elsevier, vol. 107(3), pages 740-759.
    7. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 1997. "Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model," NBER Working Papers 6250, National Bureau of Economic Research, Inc.
    8. Edmond, Chris & Weill, Pierre-Olivier, 2012. "Aggregate implications of micro asset market segmentation," Journal of Monetary Economics, Elsevier, vol. 59(4), pages 319-335.
    9. Zhigang Feng & Jianjun Miao & Adrian Peralta‐Alva & Manuel S. Santos, 2014. "Numerical Simulation Of Nonoptimal Dynamic Equilibrium Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(1), pages 83-110, February.
    10. Claudio Mattalia, 2003. "Existence of solutions and asset pricing bubbles in general equilibrium models," ICER Working Papers - Applied Mathematics Series 02-2003, ICER - International Centre for Economic Research.
    11. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    12. YiLi Chien & Hanno Lustig, 2010. "The Market Price of Aggregate Risk and the Wealth Distribution," The Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1596-1650, April.
    13. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    14. Guvenen, Fatih, 2006. "Reconciling conflicting evidence on the elasticity of intertemporal substitution: A macroeconomic perspective," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1451-1472, October.
    15. Stahn, Hubert, 1998. "On monopolistic equilibria with incomplete markets: the case of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 83-107, January.
    16. repec:dau:papers:123456789/5374 is not listed on IDEAS
    17. Jack Favilukis & Sydney C. Ludvigson & Stijn Van Nieuwerburgh, 2017. "The Macroeconomic Effects of Housing Wealth, Housing Finance, and Limited Risk Sharing in General Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 140-223.
    18. Bottazzi, Jean-Marc, 1995. "Existence of equilibria with incomplete markets: The case of smooth returns," Journal of Mathematical Economics, Elsevier, vol. 24(1), pages 59-72.
    19. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
    20. Panageas, Stavros, 2020. "The Implications of Heterogeneity and Inequality for Asset Pricing," Foundations and Trends(R) in Finance, now publishers, vol. 12(3), pages 199-275, November.
    21. Grand, François Le & Ragot, Xavier, 2018. "A class of tractable incomplete-market models for studying asset returns and risk exposure," European Economic Review, Elsevier, vol. 103(C), pages 39-59.

    More about this item

    Keywords

    Incomplete market; Financial-market equilibrium; Computation; Recursive methods;
    All these keywords.

    JEL classification:

    • 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
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cpr:ceprdp:7138. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://www.cepr.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.