Malliavin calculus for Markov chains and counterparty risk.

Summary This thesis deals with two areas of stochastic analysis and financial mathematics: the Malliavin calculus for Markov chains (Part I) and counterparty risk (Part II). Part I aims at studying the Malliavin calculus for Markov chains in continuous time. Two points are presented: proving the existence of the density for the solutions of a stochastic differential equation and computing the sensitivities of derivatives. Part II deals with current topics in the field of market risk, namely XVA (price adjustments) and multi-curve modeling.