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Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty

Author

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  • Patrick Beissner

    (Australian National University)

  • Frank Riedel

    (Bielefeld University
    University of Johannesburg)

Abstract

In diffusion models, a 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 a few long-lived assets.

Suggested Citation

  • Patrick Beissner & Frank Riedel, 2018. "Non-implementability of Arrow–Debreu equilibria by continuous trading under volatility uncertainty," Finance and Stochastics, Springer, vol. 22(3), pages 603-620, July.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:3:d:10.1007_s00780-018-0362-x
    DOI: 10.1007/s00780-018-0362-x
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    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G1 - Financial Economics - - General Financial Markets

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