We study such important properties of f -divergence minimal martingale measure as Levy preservation property, scaling property, invariance in time property for exponential Levy models. We give some useful decomposition for fdivergence minimal martingale measures and we answer on the question which form should have f to ensure mentioned properties. We show that f is not necessarily common f -divergence. For common f -divergences, i.e. functions verifying f ′′ (x) = ax γ , a > 0, γ ∈ R, we give necessary and sufficient conditions for existence of f -minimal martingale measure.
We present a unified approach to get explicit formulas for utility maximising strategies in Exponential Levy models. This approach is related to f -divergence minimal martingale measures and based on a new concept of preservation of the Levy property by f -divergence minimal martingale measures. For common fdivergences, i.e. functions which satisfy f ′′ (x) = ax γ , a > 0, γ ∈ R, we give the conditions for the existence of corresponding u f -maximising strategies, as well as explicit formulas.
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