In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa (2011) for continuous processes, we propose a framework enabling to (asymptotically) optimize the discretization times. More precisely, a discretization rule is said to be optimal if for a given cost function, no strategy has (asymptotically, for large cost) a lower mean square discretization error
for a smaller cost. We focus on discretization rules based on hitting times and give explicit expressions for the optimal rules within this class. This is a joint work with Mathieu Rosenbaum (Université Pierre et Marie Curie).