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.

在离散时间设置中，我们研究为某些金融产品提供公平价格的核心问题。这个问题主要是使用鞅度量和无套利条件来处理的。我们提出了一种基于凸对偶而不是鞅测度对偶的不同方法：价格使用 Fenchel 共轭和双共轭表示，而不使用任何无套利条件。超级对冲问题的解决会内生地导致一种称为缺乏瞬时利润 (AIP) 的弱无套利条件，在该条件下价格是有限的。我们详细研究了这个条件，提出了几个特征并将其与通常的无套利条件 NA 进行比较。