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Necessary and Sufficient Condition for the Existence of Equilibrium in Finite Dimensional Asset Markets with Short-Selling and Preferences with Half-Lines

Author

Listed:
  • Thai Ha-Huy

    (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay)

  • Cuong Le Van

    (IPAG Business School, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Myrna Wooders

    (Vanderbilt University [Nashville])

Abstract

We consider a pure exchange asset model with a finite number of agents and a finite number of states of nature where short sells are allowed. We present the definition of weak no-arbitrage price, a weaker notion of noarbitrage price than the one of Werner, and prove that if the utility functions satisfy the maximal and closed gradients conditions we propose in this paper, then there exists an equivalence between existence of a general equilibrium and existence of a price which is weak no-arbitrage price for all the agents.

Suggested Citation

  • Thai Ha-Huy & Cuong Le Van & Myrna Wooders, 2023. "Necessary and Sufficient Condition for the Existence of Equilibrium in Finite Dimensional Asset Markets with Short-Selling and Preferences with Half-Lines," Working Papers hal-04131008, HAL.
    • Handle: RePEc:hal:wpaper:hal-04131008
    Note: View the original document on HAL open archive server: https://hal.science/hal-04131008
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    References listed on IDEAS

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    Keywords

    asset market equilibrium; individually rational attainable allocations; individually rational utility set; no-arbitrage prices; no-arbitrage condition;
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