Existence of equilibrium on asset markets with a countably infinite number of states

Journal article: We consider a model with a countably infinite number of states of nature. The agents have equivalent probability beliefs and von Neumann–Morgenstern utilities. The No-Arbitrage Prices in this paper are, up to a scalar, the marginal utilities. We introduce the Beliefs Strong Equivalence and the No Half Line Condition of the same type conditions. Under these conditions, the No Arbitrage price condition is sufficient for the existence of an equilibrium when the commodity space is lp,1≤p<+∞. This No Arbitrage condition is necessary and sufficient for the existence of equilibrium when the total endowment is in l∞. Moreover, it is equivalent to the compactness of the individually rational utility set.

Author(s)

Thai Ha-Huy, Cuong Le Van

Journal
  • Journal of Mathematical Economics
Date of publication
  • 2017
Keywords JEL
C2 D50 D81 D84 G1
Keywords
  • Asset market equilibrium
  • Beliefs strong equivalence
  • Individually rational attainable allocations
  • Individually rational utility set
  • No-arbitrage condition
  • No-arbitrage prices
Pages
  • 44-53
Version
  • 1
Volume
  • 73