- FR
- EN
Discrete-Time Asset Pricing: From No-Arbitrage to Absence of Instantaneous Profit.
Abstract
Giving a fair price for a financial asset is a central question in economics and finance. The selling price should be sufficient to establish a hedging strategy for a given asset. In a discrete-time framework, this problem is traditionally solved under the No-Arbitrage (NA) assumption, which assumes rational market participants with uniform access to information. NA is equivalent to the existence of at least one risk-neutral probability measure under which the asset’s price process becomes a martingale, facilitating the calculation of the super-hedging price. However, this assumption can be questionable, as it relies on idealized rationality and information uniformity. Additionally, identifying risk-neutral measures or determining the distribution of the asset’s payoff can be computationally challenging.
To address these limitations, a weaker assumption known as the Absence of Instantaneous Profit (AIP) has been proposed. AIP requires only that prices remain finite, which is more realistic and flexible in many settings. In 2022, Emmanuel Lépinette and Laurence Carassus introduced the AIP condition and proposed a dynamic pricing approach within a discrete, frictionless framework using convex duality rather than martingale measures.
In this talk, I will discuss the transition from NA to AIP and present the mathematical resolution under each assumption.
