In this talk, we start from an arbitrage free financial model and we allow the investor to use strategies adapted with respect to a larger filtration. We first give a large class of examples when the investor makes arbitrages. Then, we present some cases where the investor can make profit, but not arbitrages. We conclude, in the case of progressive enlargement case, with a necessary and sufficient condition so that there are no arbitrages of the first kind in the enlarged filtration.

This presentation is based on a series of papers with A. Aksamit, T. Choulli, J. Deng, C. Fontana and S. Song

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