Reference

Thai Ha-Huy, Cuong Le Van, and Manh-Hung Nguyen, Arbitrage and asset market equilibrium in infinite dimensional economies with risk-averse expected utilities, April 2013.

Abstract

We consider a model with an infinite numbers of states of nature, von Neumann - Morgenstern utilities and where agents have different prob- ability beliefs. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. How- ever, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U. We give examples of non-existence of equilibrium when these conditions do not hold.

Keywords

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

JEL codes

  • C62: Existence and Stability Conditions of Equilibrium
  • D50: General
  • D81: Criteria for Decision-Making under Risk and Uncertainty
  • D84: Expectations • Speculations
  • G1: General Financial Markets

Thai Ha-Huy, Cuong Le Van, and Manh-Hung Nguyen, Arbitrage and asset market equilibrium in infinite dimensional economies with risk-averse expected utilities, Mathematical Social Sciences, vol. 79, January 2016, pp. 30–39.