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

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-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 when the utility is exponential. We illustrate our results considering the Black-Scholes model with change-point.

Key words and phrases: f-divergence, exponential Levy models, change-point, optimal portfolio

MSC 2010 subject classifications: 60G46, 60G48, 60G51, 91B70