  We consider utility maximization problem for semi-martingale models depending
on a random factor $\xi$. We reduce initial maximization problem to the
conditional one, given $\xi=u$, which we solve using dual approach. For HARA
utilities we consider information quantities like Kullback-Leibler information
and Hellinger integrals, and corresponding information processes. As a
particular case we study exponential Levy models depending on random factor. In
that case the information processes are deterministic and this fact simplify
very much indifference price calculus. Then we give the equations for
indifference prices. We show that indifference price for seller and minus
indifference price for buyer are risk measures. Finally, we apply the results
to Geometric Brownian motion case. Using identity in law technique we give the
explicit expression for information quantities. Then, the previous formulas for
indifference price can be applied.
