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Pricing rules and Arrow–Debreu ambiguous valuation

Author

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  • Aloisio Araujo
  • Alain Chateauneuf
  • 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.
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Suggested Citation

  • Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 1-35, January.
  • Handle: RePEc:spr:joecth:v:49:y:2012:i:1:p:1-35
    DOI: 10.1007/s00199-011-0660-4
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Aloisio Araujo, 2015. "General equilibrium, preferences and financial institutions after the crisis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 217-254, February.
    2. Patrick Bei{ss}ner, 2012. "Coherent Price Systems and Uncertainty-Neutral Valuation," Papers 1202.6632, arXiv.org.
    3. Beißner, Patrick, 2013. "Coherent Price Systems and Uncertainty-Neutral Valuation," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 80010, Verein für Socialpolitik / German Economic Association.
    4. Beißner, Patrick & Riedel, Frank, 2016. "Knight-Walras equilibria," Center for Mathematical Economics Working Papers 558, Center for Mathematical Economics, Bielefeld University.
    5. Georgios Gerasimou, 2015. "A Characterization of Risk-Neutral and Ambiguity-Averse Behavior," Discussion Paper Series, Department of Economics 201511, Department of Economics, University of St. Andrews, revised 10 Dec 2015.
    6. repec:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-015-2079-y is not listed on IDEAS
    7. repec:eee:jetheo:v:173:y:2018:i:c:p:257-288 is not listed on IDEAS
    8. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 33-58, May.
    9. Marcello Basili & Carlo Zappia, 2018. "Ellsberg’s Decision Rules and Keynes’s Long-Term Expectations," Department of Economics University of Siena 777, Department of Economics, University of Siena.

    More about this item

    Keywords

    Pricing rule; Frictionless incomplete market; Ambiguity; State price; Capacity; Lehrer integral; Choquet integral; D52; D53;

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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