In this work, we consider the hedging error due to discrete trading in models
with jumps. Extending an approach developped 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.

We consider the model y=X\theta+e, Z=X+v, where the n-dimensional random
vector y and the n*p random matrix Z are observed, the n*p matrix X is unknown,
v is an n*p random noise matrix, e is a noise independent of v, and \theta is a
vector of unknown parameters to be estimated. The matrix uncertainty is in the
fact that X is observed with additive error. For dimensions p that can be much
larger than the sample size n we consider the estimation of sparse vectors
\theta.