Contributions to simulation and analysis of process discretization, and applications.

Summary We present some contributions to the simulation and analysis of process discretization, with their applications in finance. We have grouped our work into 4 themes: 1. statistics of processes with discrete observations. 2. Discrete time coverage in finance. 3. Sensitivities of expectations. 4. discretization error analysis. The first chapter on process statistics is quite independent from the rest. On the other hand, the three other chapters correspond to a coherence and a progression in the questions raised. Nevertheless, as you read the book, you will notice links between the four parts: differentiation with respect to domains and improvement of output time simulation, expectation sensitivities and asymptotic statistics with Malliavin's calculus, expectation sensitivities and error analysis etc. The proofs of the results are based on the tools of Malliavin calculus, martingales, Partial Differential Equations and their links with Stochastic Differential Equations.