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Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling

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  • Dana, R.A.
  • Le Van, C.

Abstract

The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. No-arbitrage conditions are given in terms of risk adjusted priors. A sufficient condition for existence of efficient allocations is the overlapping of the interiors of the risk adjusted sets of priors or the inexistence of mutually compatible trades, with non-negative expectation with respect to any risk adjusted prior. These conditions are necessary when agents are not risk neutral at extreme levels of wealths. It is shown that the more uncertainty averse or risk averse the agents, the more likely are efficient allocations and equilibria to exist.

Suggested Citation

  • Dana, R.A. & Le Van, C., 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2186-2202, November.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:6:p:2186-2202
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    More about this item

    Keywords

    Uncertainty Risk Common prior Equilibria with short-selling Variational preferences;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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