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Incomplete markets with a countable number of states: Equilibrium and No-Arbitrage

Author

Listed:
  • Jean-Marc Bonnisseau

    (UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, 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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Cuong Le Van

    (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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, IPAG Business School, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Cuong TRAN VIET

Abstract

In this paper, we prove the existence of an equilibrium in a two-period model à la Hart with incomplete markets and a countable number of states under a mild restriction on the asymptotic behaviour of the returns matrix. Then, we show that an equilibrium asset price is a no-arbitrage price. Conversely, we consider a sequence of equilibria à la Cass corresponding to an increasing number of states associated with a given sequence of present-values. If the sequence of commodity prices has a non-zero cluster point for the product topology, then the limits of these prices and of the allocations (assets, commodities) constitute, together with the given asset price, an equilibrium with a countable number of states.

Suggested Citation

  • Jean-Marc Bonnisseau & Cuong Le Van & Cuong TRAN VIET, 2024. "Incomplete markets with a countable number of states: Equilibrium and No-Arbitrage," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04982842, HAL.
    • Handle: RePEc:hal:cesptp:hal-04982842
    Note: View the original document on HAL open archive server: https://hal.science/hal-04982842v1
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