Submodular financial markets with frictions

Alain Chateauneuf and Bernard Cornet ()
Additional contact information
Bernard Cornet: University of Kansas

Economic Theory, 2022, vol. 73, issue 2, No 16, 744 pages

Abstract: 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)
JEL-codes: D81 G11 G12 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://link.springer.com/10.1007/s00199-022-01415-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
Working Paper: Submodular financial markets with frictions (2022)
Working Paper: Submodular financial markets with frictions (2022)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joecth:v:73:y:2022:i:2:d:10.1007_s00199-022-01415-7

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/199/PS2

DOI: 10.1007/s00199-022-01415-7

Access Statistics for this article

Economic Theory is currently edited by Nichoals Yanneils

More articles in Economic Theory from Springer, Society for the Advancement of Economic Theory (SAET) Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().