An $f$-divergence approach for optimal portfolios in exponential Levy models

Abstract

We present a unified approach to get explicit formulas for utility maximising strategies in Exponential Levy models. This approach is related to $f$-divergence minimal martingale measures and based on a new concept of preservation of the Levy property by $f$-divergence minimal martingale measures. For common $f$-divergences, i.e. functions which satisfy $f"(x)= ax^ {\gamma},\, a>0, \, \gamma \in \mathbb R$, we give the conditions for the existence of corresponding $u_f$- maximising strategies, as well as explicit formulas.