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Pricing rules and Arrow–Debreu ambiguous valuation

Listed author(s):
  • Aloisio Araujo
  • Alain Chateauneuf
  • José Faro

    ()

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.

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File URL: http://hdl.handle.net/10.1007/s00199-011-0660-4
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Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 49 (2012)
Issue (Month): 1 (January)
Pages: 1-35

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Handle: RePEc:spr:joecth:v:49:y:2012:i:1:p:1-35
DOI: 10.1007/s00199-011-0660-4
Contact details of provider: Web page: http://www.springer.com

Web page: http://saet.uiowa.edu/

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