Utility maximisation and utility indifference price for exponential semi-martingale models with random factor

We consider utility maximization problem for semi-martingale models depending on a random factor $ξ$. We reduce initial maximization problem to the conditional one, given $ξ=u$, 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 determi...