Some properties of the variance-optimal martingale measure for discontinuous semimartingales

We focus on properties of the variance-optimal martingale measure for discontinuous semimartingales. In particular, we give sufficient conditions for the variance-optimal martingale measure to be a probability measure, and for the density process of the variance-optimal martingale measure to satisfy the reverse Hölder inequality, respectively. Moreover, we study relationship with mean-variance hedging.