In this work, we consider the hedging error due to discrete trading in models with jumps. We propose a framework enabling to (asymptotically) optimize the discretization times. More precisely, a strategy is said to be optimal if for a given cost function, no strategy has (asymptotically) a lower mean square error for a smaller cost. We focus on strategies based on hitting times and give explicit expressions for the optimal strategies. This is joint work with Peter Tankov.