  We study exponential Levy models with change-point which is a random
variable, independent from initial Levy processes. On canonical space with
initially enlarged filtration we describe all equivalent martingale measures
for change-point model and we give the conditions for the existence of
f-divergence minimal equivalent martingale measure. Using the connection
between utility maximisation and $f$-divergence minimisation, we obtain a
general formula for optimal strategy in change-point case for initially
enlarged filtration and also for progressively enlarged filtration in the case
of exponential utility. We illustrate our results considering the Black-Scholes
model with change-point.
