Fundamental theorem of asset pricing without reference measure

Ludovic Tangpi (Universität Konstanz)
Thursday, June 19, 2014 - 4:00pm
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

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 disappearing 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 such free lunches is equivalent to the existence of a set of local martingale measures equivalent to the set of possible models. Talk based on a joint work with Michael Kupper and Patrick Cheridito.