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Dynamic Aggregation and Computation of Equilibria in Finite-Dimensional Economies with Incomplete Financial Markets

Author

Listed:
  • Domenico Cuoco

    (The Wharton School, University of Pennsylvania)

  • Hua He

    (Yale School of Management, Yale University)

Abstract

This paper constructs a representative agent supporting the equilibrium allocation in ¡°event-tree¡± economies with time-additive preferences and possibly incomplete securities markets. If the equilibrium allocation is Pareto optimal, this construction gives the usual linear welfare function. Otherwise, the representative agent¡¯s utility function is state-dependent, even when individual agents have state-independent utilities and homogeneous beliefs. The existence of a representative agent allows us to provide a characterization of equilibria which does not rely on the derivation of the agents¡¯ intertemporal demand functions for consumption and investment and transforms the dynamic general equilibrium problem into a static one. This characterization is therefore especially well suited for numerical computation of equilibria in economies with incomplete financial markets.

Suggested Citation

  • Domenico Cuoco & Hua He, 2001. "Dynamic Aggregation and Computation of Equilibria in Finite-Dimensional Economies with Incomplete Financial Markets," Annals of Economics and Finance, Society for AEF, vol. 2(2), pages 265-296, November.
    • Handle: RePEc:cuf:journl:y:2001:v:2:i:2:p:265-296
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Robert Jarrow, 2018. "Asset market equilibrium with liquidity risk," Annals of Finance, Springer, vol. 14(2), pages 253-288, May.
    2. Jarrow, Robert & Larsson, Martin, 2018. "On aggregation and representative agent equilibria," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 119-127.
    3. Uppal, Raman & Vilkov, Grigory & Buss, Adrian, 2015. "Where Experience Matters: Asset Allocation and Asset Pricing with Opaque and Illiquid Assets," CEPR Discussion Papers 10437, C.E.P.R. Discussion Papers.
    4. Patrick Cheridito & Ulrich Horst & Michael Kupper & Traian A. Pirvu, 2016. "Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 174-195, February.
    5. Robert Jarrow & Siguang Li, 2021. "Concavity, stochastic utility, and risk aversion," Finance and Stochastics, Springer, vol. 25(2), pages 311-330, April.
    6. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," CARF F-Series CARF-F-509, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Dong Chul Won, 2019. "A New Characterization of Equilibrium in a Multi-period Finance Economy: A Computational Viewpoint," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 367-396, January.
    8. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CARF F-Series CARF-F-495, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Felix Kubler & Johannes Brumm, 2013. "Applying Negishi's method to stochastic models with overlapping generations," 2013 Meeting Papers 1352, Society for Economic Dynamics.
    10. Jaroslav Borovička, 2020. "Survival and Long-Run Dynamics with Heterogeneous Beliefs under Recursive Preferences," Journal of Political Economy, University of Chicago Press, vol. 128(1), pages 206-251.
    11. Masaaki Fujii & Akihiko Takahashi, 2021. "``Equilibrium Price Formation with a Major Player and its Mean Field Limit''," CIRJE F-Series CIRJE-F-1162, CIRJE, Faculty of Economics, University of Tokyo.
    12. Piero Gottardi & Felix Kubler, 2015. "Dynamic Competitive Economies with Complete Markets and Collateral Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 1119-1153.
    13. YiLi Chien & Harold L. Cole & Hanno Lustig, 2014. "Implications of heterogeneity in preferences, beliefs and asset trading technologies for the macroeconomy," Working Papers 2014-14, Federal Reserve Bank of St. Louis.
    14. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CIRJE F-Series CIRJE-F-1156, CIRJE, Faculty of Economics, University of Tokyo.
    15. Yili Chien & Harold Cole & Hanno Lustig, 2016. "Implications of Heterogeneity in Preferences, Beliefs and Asset Trading Technologies in an Endowment Economy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 20, pages 215-239, April.
    16. Shen, Yang & Siu, Tak Kuen, 2013. "Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 757-768.
    17. Anna Pavlova & Roberto Rigobon, 2010. "International Macro-Finance," NBER Working Papers 16630, National Bureau of Economic Research, Inc.
    18. Buss, Adrian & Uppal, Raman & Vilkov, Grigory, 2015. "Asset prices in general equilibrium with recursive utility and illiquidity induced by transactions costs," SAFE Working Paper Series 41, Leibniz Institute for Financial Research SAFE, revised 2015.
    19. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.
    20. Uppal, Raman & Bhamra, Harjoat Singh, 2006. "The Effect of Introducing a Non-redundant Derivative on the Volatility of Stock-Market Returns," CEPR Discussion Papers 5726, C.E.P.R. Discussion Papers.
    21. Masaaki Fujii & Akihiko Takahashi, 2020. "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium," Papers 2010.09186, arXiv.org, revised Dec 2021.

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    More about this item

    Keywords

    Equilibria; Aggregation; Incomplete markets;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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