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

Jean-Marc Bonnisseau (), Cuong Le Van () and Cuong Tran Viet ()
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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

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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.

Keywords: Financial Equilibrium; Infinite State Space; Incomplete Market; No-Arbitrage Prices; No-Arbitrage Condition (search for similar items in EconPapers)
Date: 2024-12
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