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Existence of Arrow-Debreu Equilibrium with Generalized Stochastic Differential Utility

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  • Beißner, Patrick

    (Center for Mathematical Economics, Bielefeld University)

Abstract

This paper establishes, in the setting of Brownian information, a general equilibrium existence result under a stochastic differential for- mulation of intertemporal recursive utility. The present class of utility functionals is generated by a backward stochastic differential equation and incorporates preference for the local risk of the stochastic utility process. The setting contains models in which Knightian uncertainty is repre- sented in the subjective and objective sense.

Suggested Citation

  • Beißner, Patrick, 2015. "Existence of Arrow-Debreu Equilibrium with Generalized Stochastic Differential Utility," Center for Mathematical Economics Working Papers 447, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:447
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    File URL: https://pub.uni-bielefeld.de/download/2900053/2900054
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    References listed on IDEAS

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    1. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
    2. Frank Riedel & Peter Bank, 2001. "Existence and structure of stochastic equilibria with intertemporal substitution," Finance and Stochastics, Springer, vol. 5(4), pages 487-509.
    3. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    4. Epstein, Larry G. & Miao, Jianjun, 2003. "A two-person dynamic equilibrium under ambiguity," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1253-1288, May.
    5. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    6. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    7. Hindy, Ayman & Huang, Chi-fu, 1992. "Intertemporal Preferences for Uncertain Consumption: A Continuous Time Approach," Econometrica, Econometric Society, vol. 60(4), pages 781-801, July.
    8. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
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    Cited by:

    1. Beißner, Patrick, 2016. "Radner Equilibria under Ambiguous Volatility," Center for Mathematical Economics Working Papers 493, Center for Mathematical Economics, Bielefeld University.

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    More about this item

    Keywords

    BSDE; GSDU; super-gradients; properness; general equilibrium; Knightian uncertainty;
    All these keywords.

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