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