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Submodular financial markets with frictions

Author

Listed:
  • Alain Chateauneuf

    (Université Paris 1)

  • Bernard Cornet

    (University of Kansas)

Abstract

This paper studies arbitrage-free financial markets with bid-ask spreads whose super-hedging prices are submodular. The submodular assumption on the super-hedging price, or the supermodularity usually assumed on utility functions, is the formal expression of perfect complementarity, which dates back to Fisher, Pareto, and Edgeworth, according to Samuelson (J Econ Lit 12:1255–1289, 1974). Our main contribution provides several characterizations of financial markets with frictions that are submodular as a consequence of a more general study of submodular pricing rules. First, a market is submodular if and only if its super-hedging price is a Choquet integral and if and only if its set of risk-neutral probabilities is representable as the core of a submodular non-additive probability that is uniquely defined, called risk-neutral capacity. Second, a market is representable by its risk neutral capacity if and only if it is equivalent to a market, only composed of bid-ask event securities.

Suggested Citation

  • Alain Chateauneuf & Bernard Cornet, 2022. "Submodular financial markets with frictions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 721-744, April.
    • Handle: RePEc:spr:joecth:v:73:y:2022:i:2:d:10.1007_s00199-022-01415-7
    DOI: 10.1007/s00199-022-01415-7
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    Cited by:

    1. Cinfrignini, Andrea & Petturiti, Davide & Vantaggi, Barbara, 2023. "Dynamic bid–ask pricing under Dempster-Shafer uncertainty," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    2. Alain Chateauneuf & Bernard Cornet, 2022. "The risk-neutral non-additive probability with market frictions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 13-25, May.
    3. Alain Chateauneuf & Bernard Cornet, 2022. "Submodular financial markets with frictions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 721-744, April.
    4. Lorenzo Bastianello & Alain Chateauneuf & Bernard Cornet, 2022. "Put-Call Parities, absence of arbitrage opportunities and non-linear pricing rules," Papers 2203.16292, arXiv.org.
    5. Rabah Amir & Bernard Cornet & M. Ali Khan & David Levine & Edward C. Prescott, 2022. "Special Issue in honor of Nicholas C. Yannelis – Part II," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 377-385, April.

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    More about this item

    Keywords

    Submodularity; financial markets; Frictions; Bid-ask; Arbitrage; Multi-prior model; Super-hedging price; Super-replication; Risk measure; Pricing rules; Choquet integral; Event securities;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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