Incomplete Markets with a Countable Number of States: Equilibrium and No-Arbitrage

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

Annals of Economics and Statistics, 2025, issue 159, 35-78

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)
JEL-codes: D52 D53 G11 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:adr:anecst:y:2025:i:159:p:35-78

DOI: 10.2307/48839154

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