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Endogenous completeness of diffusion driven equilibrium markets

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  • Julien HUGONNIER

    (Ecole Polytechnique Federale de Lausanne and Swiss Finance Institute)

  • Semyon MALAMUD

    (Ecole Polytechnique Federale de Lausanne and Swiss Finance Institute)

  • Eugene TRUBOWITZ

    (ETH Zurich)

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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Bibliographic Info

Paper provided by Swiss Finance Institute in its series Swiss Finance Institute Research Paper Series with number 09-41.

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Length: 77 pages
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Handle: RePEc:chf:rpseri:rp0941

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Web page: http://www.SwissFinanceInstitute.ch
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Keywords: continuous-time finance; dynamic market completeness; general equilibrium theory.;

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Cited by:
  1. Theodoros M. Diasakos, 2012. "A Simple Characterization of Dynamic Completeness in Continuous Time," Discussion Paper Series, Department of Economics 201312, Department of Economics, University of St. Andrews, revised 02 Sep 2013.
  2. 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.
  3. Frederik Herzberg & Frank Riedel, 2012. "Existence of Financial Equilibria in Continuous Time with Potentially Complete Markets," Papers 1207.2010, arXiv.org.
  4. Dmitry Kramkov, 2013. "Existence of an endogenously complete equilibrium driven by a diffusion," Papers 1304.3516, arXiv.org.
  5. Hugonnier, Julien, 2012. "Rational asset pricing bubbles and portfolio constraints," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2260-2302.
  6. Martin Larsson, 2013. "Non-Equivalent Beliefs and Subjective Equilibrium Bubbles," Papers 1306.5082, arXiv.org.
  7. 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.

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