This article is devoted to the maximization of HARA utilities of Lévy
switching process on finite time interval via dual method. We give the description
of all f-divergence minimal martingale measures in progressively enlarged
filtration, the expression of their Radon-Nikodym densities involving Hellinger
and Kulback-Leibler processes, the expressions of the optimal strategies for
the maximization of HARA utilities as well as the values of the corresponding
maximal expected utilities. The example of Brownian switching models is presented.
This is common work with Lioudmila Vostrikova.