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Endogenous Completeness of Diffusion Driven Equilibrium Markets

Author

Listed:
  • J. Hugonnier
  • S. Malamud
  • E. Trubowitz

Abstract

We study the existence of equilibria with endogenously complete markets in a continuous-time, heterogenous agents economy driven by a multidimensional diffusion process. Our main results show that if prices are real analytic as functions of time and the state variables of the model then a suffi- cient condition for market completeness is that the volatility of dividends be nondegenerate. In contrast to previous research, our formulation does not require that securities pay terminal dividends and thus allows for both finite or infinite horizon economies. We illustrate our results by providing easily applicable conditions for market completeness in two benchmark cases: that where the state variables are given by a vector autoregressive process and that where they are given by a vector of autonomous diffusion processes. We also provide counterexamples which show that real analyticity cannot be dispensed with if one is to deduce dynamic market completeness from the structure of dividends.
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Suggested Citation

  • J. Hugonnier & S. Malamud & E. Trubowitz, 2012. "Endogenous Completeness of Diffusion Driven Equilibrium Markets," Econometrica, Econometric Society, vol. 80(3), pages 1249-1270, May.
  • Handle: RePEc:ecm:emetrp:v:80:y:2012:i:3:p:1249-1270
    DOI: ECTA8783
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    File URL: http://hdl.handle.net/10.3982/ECTA8783
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    Citations

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    Cited by:

    1. Riedel, Frank & Herzberg, Frederik, 2013. "Existence of financial equilibria in continuous time with potentially complete markets," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 398-404.
    2. Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
    3. Kasper Larsen & Tanawit Sae Sue, 2015. "Radner equilibrium in incomplete Levy models," Papers 1507.02974, arXiv.org, revised Jul 2015.
    4. repec:eee:mateco:v:74:y:2018:i:c:p:119-127 is not listed on IDEAS
    5. Martin Larsson, 2013. "Non-Equivalent Beliefs and Subjective Equilibrium Bubbles," Papers 1306.5082, arXiv.org.
    6. Roman Muraviev, 2013. "Market selection with learning and catching up with the Joneses," Finance and Stochastics, Springer, vol. 17(2), pages 273-304, April.
    7. Dmitry Kramkov & Silviu Predoiu, 2011. "Integral representation of martingales motivated by the problem of endogenous completeness in financial economics," Papers 1110.3248, arXiv.org, revised Oct 2012.
    8. Daniel C. Schwarz, 2015. "Market Completion with Derivative Securities," Papers 1506.00188, arXiv.org.
    9. Patrick Beissner & Frank Riedel, 2014. "Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty," Papers 1409.6940, arXiv.org.
    10. Theodoros M. Diasakos, 2011. "A Simple Characterization of Dynamic Completeness in Continuous Time," Carlo Alberto Notebooks 211, Collegio Carlo Alberto.
    11. Kramkov, Dmitry & Predoiu, Silviu, 2014. "Integral representation of martingales motivated by the problem of endogenous completeness in financial economics," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 81-100.
    12. Hansen, Simon Lysbjerg, 2015. "Cross-sectional asset pricing with heterogeneous preferences and beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 125-151.
    13. Daniel C. Schwarz, 2017. "Market completion with derivative securities," Finance and Stochastics, Springer, vol. 21(1), pages 263-284, January.
    14. Dmitry Kramkov, 2013. "Existence of an endogenously complete equilibrium driven by a diffusion," Papers 1304.3516, arXiv.org, revised Oct 2014.
    15. Dmitry Kramkov, 2015. "Existence of an endogenously complete equilibrium driven by a diffusion," Finance and Stochastics, Springer, vol. 19(1), pages 1-22, January.
    16. Peter Bank & Dmitry Kramkov, 2015. "A model for a large investor trading at market indifference prices. I: Single-period case," Finance and Stochastics, Springer, vol. 19(2), pages 449-472, April.
    17. Alziary Chassat, Bénédicte & Takac, Peter, 2017. "On the Heston Model with Stochastic Volatility: Analytic Solutions and Complete Markets," TSE Working Papers 17-796, Toulouse School of Economics (TSE).

    More about this item

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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