Pricing without no-arbitrage condition in discrete time
Carassus, Laurence; Lépinette, Emmanuel (2021), Pricing without no-arbitrage condition in discrete time, Journal of Mathematical Analysis and Applications, 505, 1. 10.1016/j.jmaa.2021.125441
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Analysis and Applications
MetadataShow full item record
Laboratoire de Mathématiques de Reims [LMR]
Laboratoire de Probabilités, Statistique et Modélisation [LPSM (UMR_8001)]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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.
Subjects / KeywordsFinancial market models; Super-hedging prices; AIP condition; Conditional support; Essential supremum.
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