Submodular financial markets with frictions

Alain Chateauneuf and Bernard Cornet
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Bernard Cornet: KU - University of Kansas [Lawrence], 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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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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.

Keywords: Submodularity; financial markets; Frictions; Bid-ask; Arbitrage; Multi-prior model; Super-hedging price; Super-replication; Risk measure; Pricing rules; Choquet integral; Event securities (search for similar items in EconPapers)
Date: 2022
New Economics Papers: this item is included in nep-upt
Note: View the original document on HAL open archive server: https://hal.science/hal-03722920
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Published in Economic Theory, 2022, 73 (2-3), pp.721-744. ⟨10.1007/s00199-022-01415-7⟩

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Journal Article: Submodular financial markets with frictions (2022)
Working Paper: Submodular financial markets with frictions (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03722920

DOI: 10.1007/s00199-022-01415-7

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