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

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