Pricing rules and Arrow-Debreu ambiguous valuation

Article dans une revue: This paper considers pricing rules of single-period securities markets with finitely many states. Our main result characterizes those pricing rules C that are super-replication prices of a frictionless and arbitrage-free incomplete asset structure with a bond. This characterization relies on the equivalence between the sets of frictionless securities and securities priced by C. The former captures securities without bid-ask spreads, while the second captures the class of securities where, if some of its delivers is replaced by a higher payoff, then the resulting security is characterized by a higher value priced by C. We also analyze the special case of pricing rules associated with securities markets admitting a structure of basic assets paying one in some event and nothing otherwise. In this case, we show that the pricing rule can be characterized in terms of capacities. This Arrow-Debreu ambiguous state price can be viewed as a generalization for incomplete markets of Arrow-Debreu state price valuation. Also, some interesting cases are given by pricing rules determined by an integral w.r.t. a risk-neutral capacity. For instance, incomplete markets of Arrow securities and a bond are revealed by a Choquet integral w.r.t. a special risk-neutral capacity.

Auteur(s)

Aloisio Araujo, Alain Chateauneuf, José Heleno Faro

Revue
  • Economic Theory
Date de publication
  • 2012
Mots-clés JEL
D.D5.D52
Mots-clés
  • Ambiguity
  • Capacity
  • Lehrer integral
  • Choquet integral
  • Frictionless incomplete market
  • Pricing rule
  • State price
Pages
  • 1-35
Version
  • 1
Volume
  • 49