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Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Volatility Uncertainty

Author

Listed:
  • Beißner, Patrick

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In diffusion models, few suitably chosen financial securities allow to complete the market. As a consequence, the efficient allocations of static Arrow-Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow-Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow-Debreu equilibrium allocations are generically unattainable by dynamically trading few long-lived assets.

Suggested Citation

  • Beißner, Patrick & Riedel, Frank, 2025. "Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Volatility Uncertainty," Center for Mathematical Economics Working Papers 707, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:707
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    File URL: https://pub.uni-bielefeld.de/download/3004387/3004389
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    References listed on IDEAS

    as
    1. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
    2. 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.
    3. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
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    5. Robert M. Anderson & Roberto C. Raimondo, 2008. "Equilibrium in Continuous-Time Financial Markets: Endogenously Dynamically Complete Markets," Econometrica, Econometric Society, vol. 76(4), pages 841-907, July.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    Full references (including those not matched with items on IDEAS)

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