Levy preservation and associated properties for $f$-divergence minimal equivalent martingale measures

Details Levy preservation and associated properties for $f$-divergence minimal equivalent martingale measures Levy preservation and associated properties for $f$-divergence minimal equivalent martingale measures

2011-06-14

arxiv.org/abs/1106.2743v1

Mathematics

Probability

30 pages, no figures

Scientific paper

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 $f$-divergence 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 $f"(x) = ax^ {\gamma},\, a>0,\, \gamma \in \mathbb R$, we give necessary and sufficient conditions for existence of $f$-minimal martingale measure.

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