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We study exponential Levy models with change-point which is a randomvariable, independent from initial Levy processes. On canonical space withinitially enlarged filtration we describe all equivalent martingale measuresfor change-point model and we give the conditions for the existence off-divergence minimal equivalent martingale measure. Using the connectionbetween utility maximisation and $f$-divergence minimisation, we obtain ageneral formula for optimal strategy in change-point case for initiallyenlarged filtration and also for progressively enlarged filtration in the caseof exponential utility. We illustrate our results considering the Black-Scholesmodel with change-point.

$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point