Minimax and minimal distance martingale measures and their relationship to portfolio optimization

In this paper we give a characterization of minimal distance martingale measures with respect to f-divergence distances in a general semimartin-gale market model. We provide necessary and suucient conditions for minimal distance martingale measures and determine them explicitly for exponential L evy processes with respect to several classical distances. It is shown that the minimal distance martingale measures are equivalent to minimax martingale measures with respect to related utility functions and that optimal portfolios can be characterized by them. Related results in the context of continuous-time diiusion models were rst obtained by He and Pearson (1991b) and Karatzas et al. (1991) and in a general semi-martingale setting by Kramkov and Schachermayer (1999). Finally parts of the results are extended to utility-based hedging.