Pricing without no-arbitrage condition in discrete time

In a discrete time setting, we study the central problem of giving a fair price to some financial product. This problem has been mostly treated using martingale measures and no-arbitrage conditions. We propose a different approach based on convex duality instead of martingale measures duality: The p...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2022-01, Vol.505 (1), p.125441, Article 125441
Main Authors: Carassus, Laurence, Lépinette, Emmanuel
Format: Article
Language:English
Subjects:
AIP condition
Conditional support
Essential supremum
Financial market models
Mathematics
Probability
Super-hedging prices
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Summary:In a discrete time setting, we study the central problem of giving a fair price to some financial product. This problem has been mostly treated using martingale measures and no-arbitrage conditions. We propose a different approach based on convex duality instead of martingale measures duality: The prices are expressed using Fenchel conjugate and bi-conjugate without using any no-arbitrage condition. The super-hedging problem resolution leads endogenously to a weak no-arbitrage condition called Absence of Instantaneous Profit (AIP) under which prices are finite. We study this condition in detail, propose several characterizations and compare it to the usual no-arbitrage condition NA.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125441