  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.

Probability