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Pricing rules and Arrow-Debreu ambiguous valuation

Aloisio Araujo, Alain Chateauneuf () and José Faro ()

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Abstract: 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.

Keywords: Ambiguity; Capacity; Lehrer integral; Choquet integral; Frictionless incomplete market; Pricing rule; State price (search for similar items in EconPapers)
Date: 2012-01
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Published in Economic Theory, Springer Verlag, 2012, 49 (1), pp.1-35. ⟨10.1007/s00199-011-0660-4⟩

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DOI: 10.1007/s00199-011-0660-4

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