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

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  • Jean-Marc Bonnisseau
  • Cuong Le Van
  • 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, 2025. "Incomplete Markets with a Countable Number of States: Equilibrium and No-Arbitrage," Annals of Economics and Statistics, GENES, issue 159, pages 35-78.
    • Handle: RePEc:adr:anecst:y:2025:i:159:p:35-78
    DOI: 10.2307/48839154
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    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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