Random times, enlargement of filtration and arbitrages.

Summary This thesis treats the problems settled in enlargement of filtraion theory. It consists of two parts. The first part is devoted to random times. We study the properties of different classes of random times from enlargement of filtration point of view. The second part concerns the study of the stability of the no arbitrage condition under enlargement of filtration. We are mainly interested in No Unbounded Profit with Bounded Risk condition. We study absence of arbitrage in the case of progressive enlargement of up to random time. Then we look at the case of initial enlargement with random variable satisfying Jacod's hypothesis.