Pricing Rules and Arrow Debreu Ambiguous Valuation

34 Pages Posted: 3 Oct 2013

See all articles by Aloisio Araujo

Aloisio Araujo

Getulio Vargas Foundation (FGV) - FGV/EPGE Escola Brasileira de Economia e Finanças

Alain Chateauneuf

University of Paris

José Heleno Faro

Insper Institute of Education and Research

Date Written: June 20, 2010

Abstract

This paper considers pricing rules of single-period securities markets with finitely many states and without arbitrage opportunities. Our main result characterize those pricing rules C that are super-replication prices of a frictionless incomplete asset structure. This characterization relies on the equivalence between the sets of frictionless securities and undominated 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 revealing securities markets admitting a structure of basic assets paying one in some event and nothing otherwise. In this case we show that any security can be priced against a capacity. This risk-neutral capacity, or Arrow-Debreu ambiguous state price, can be viewed as a generalization for incomplete markets of Arrow Debreu price valuation, and the corresponding pricing rule is determined by an integral w.r.t. a subadditive capacity. For instance, a special class of Choquet integral is related to frictionless incomplete markets of Arrow securities and a riskless asset.

Keywords: Pricing rule, frictionless incomplete market, ambiguity

JEL Classification: D52, D53

Suggested Citation

Araujo, Aloisio and Chateauneuf, Alain and Faro, José Heleno, Pricing Rules and Arrow Debreu Ambiguous Valuation (June 20, 2010). Economic Theory, Vol. 49, No. 1, 2012, Available at SSRN: https://ssrn.com/abstract=2330296

Aloisio Araujo (Contact Author)

Getulio Vargas Foundation (FGV) - FGV/EPGE Escola Brasileira de Economia e Finanças ( email )

Praia de Botafogo 190/1125, CEP
Rio de Janeiro RJ 22253-900
Brazil

Alain Chateauneuf

University of Paris ( email )

DEA MMME
106-112, Boulevard de l'Hopital
Paris cedex 13, 75647
France

José Heleno Faro

Insper Institute of Education and Research ( email )

R Quata 300
Sao Paulo, 04542-030
Brazil

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