Asymptotically optimal discretization of hedging strategies with jumps

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).