  This article is devoted to the maximisation of HARA utilities of L{\'e}vy
switching process on finite time interval via dual method. We give the
description of all f-divergence minimal martingale measures in initially
enlarged filtration, the expression of their Radon-Nikodym densities involving
Hellinger and Kulback-Leibler processes, the expressions of the optimal
strategies in progressively enlarged filtration for the maximisation of HARA
utilities as well as the values of the corresponding maximal expected
utilities. The example of Brownian switching model is presented to give the
financial interpretation of the results.
