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Pricing rules and Arrow-Debreu ambiguous valuation

Author

Listed:
  • Aloisio Araujo
  • Alain Chateauneuf

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • José Heleno Faro

    (CEDEPLAR - Centre for Development and Regional Planning - UFMG - Universidade Federal de Minas Gerais = Federal University of Minas Gerais)

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.

Suggested Citation

  • Aloisio Araujo & Alain Chateauneuf & José Heleno Faro, 2012. "Pricing rules and Arrow-Debreu ambiguous valuation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00685413, HAL.
    • Handle: RePEc:hal:cesptp:hal-00685413
    DOI: 10.1007/s00199-011-0660-4
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    Cited by:

    1. Gianluca Cassese, 2021. "Complete and competitive financial markets in a complex world," Finance and Stochastics, Springer, vol. 25(4), pages 659-688, October.
    2. Aloisio Araujo & Alain Chateauneuf & José Heleno Faro & Bruno Holanda, 2019. "Updating pricing rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 335-361, September.
    3. 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.
    4. Antoine Billot & Sujoy Mukerji & Jean-Marc Tallon, 2020. "Market Allocations under Ambiguity: A Survey," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 267-282.
    5. Beißner, Patrick, 2013. "Coherent Price Systems and Uncertainty-Neutral Valuation," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 80010, Verein für Socialpolitik / German Economic Association.
    6. Beißner, Patrick & Riedel, Frank, 2016. "Knight-Walras equilibria," Center for Mathematical Economics Working Papers 558, Center for Mathematical Economics, Bielefeld University.
    7. Gerasimou, Georgios, 2015. "A Characterization of Risk-Neutral and Ambiguity-Averse Behavior," MPRA Paper 68159, University Library of Munich, Germany.
    8. Tarik Driouchi & Lenos Trigeorgis & Raymond H. Y. So, 2018. "Option implied ambiguity and its information content: Evidence from the subprime crisis," Annals of Operations Research, Springer, vol. 262(2), pages 463-491, March.
    9. Marcello Basili & Alain Chateauneuf & Giuseppe Scianna, 2019. "A consistent representation of Keynes’s long-term expectation in ?nancial market," Department of Economics University of Siena 808, Department of Economics, University of Siena.
    10. Araujo, Aloisio & Chateauneuf, Alain & Faro, José Heleno, 2018. "Financial market structures revealed by pricing rules: Efficient complete markets are prevalent," Journal of Economic Theory, Elsevier, vol. 173(C), pages 257-288.
    11. 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.
    12. 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.
    13. Gerasimou, Georgios, 2015. "A Characterization of Risk-Neutral and Ambiguity-Averse Behavior," MPRA Paper 68159, University Library of Munich, Germany.
    14. Patrick Bei{ss}ner, 2012. "Coherent Price Systems and Uncertainty-Neutral Valuation," Papers 1202.6632, arXiv.org.
    15. Alain Chateauneuf & Bernard Cornet, 2025. "Financial Markets With Hedging Complements," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202510, University of Kansas, Department of Economics.
    16. Hu, Wei & Zheng, Zhenlong, 2020. "Expectile CAPM," Economic Modelling, Elsevier, vol. 88(C), pages 386-397.
    17. Marcello Basili & Alain Chateauneuf & Giuliano Antonio & Giuseppe Scianna, 2023. "A representation of Keynes's long-term expectation in financial markets," Working Papers hal-03999320, HAL.
    18. Lécuyer, Emy & Riedel, Frank & Stanca, Lorenzo, 2024. "Arbitrage Pricing in Convex, Cash-Additive Markets," Center for Mathematical Economics Working Papers 694, Center for Mathematical Economics, Bielefeld University.

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    JEL classification:

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

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