Contributions to the study of discretization of processes with jumps, liquidity risk, and jump risk in financial markets.

Summary This paper summarizes my contributions to the study of discretization of processes with jumps, and to the modeling of liquidity risk and jump risk in financial markets. Chapter 2 gathers more theoretical results in the field of discretization of stochastic processes with jumps, with in particular a study of the discretization error of hedging strategies, and new simulation schemes of stochastic differential equations directed by Lévy processes. Chapter 3 presents and studies via stochastic control an investment and consumption optimization problem in illiquid financial markets. Chapter 4 contains more applied work on modeling jump risk in portfolio insurance strategies, derivatives, and electricity markets.