Abstracts

When a financial market is governed by a single probability measure, the absence of arbitrage opportunities is characterized by the existence of equivalent martingale or local martingale measures. In this talk, we focus on the fundamental theorem of asset pricing in the case where the market is governed by a non-dominated set of probability measures. We introduce the concept of free lunch with controlled risk. Our main result shows that, in a continuous time model, if the agent is allowed to trade only with strategies that are simple integrands, then the absence of free lunches with controlled risk is equivalent to the existence of a set of local martingale measures equivalent to the set of possible models. Talk based on a join work with Michael Kupper and Patrick Cheridito.