  In this work, we consider the hedging error due to discrete trading in models
with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis
with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG]
for continuous processes, we propose a framework enabling us 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.
