Weak and strong arbitrage opportunities and enlargements of filtrations.

In the context of a general continuous financial market model, we study whether the additional information associated to a random time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we show that this depends on the properties of the random time under consideration. In particular, we study the case of an honest time T and we show explicitly that arbitrage profits can never be realized strictly before T, while classical arbitrage opportunities can be realized exactly at T and stronger arbitrages of the first kind always exist after T. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR. Based on joint work with M. Jeanblanc and S. Song