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

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### Abstract

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.

### Most cited references4

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### Minimal Hellinger martingale measures of order q

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### MINIMAL ENTROPY-HELLINGER MARTINGALE MEASURE IN INCOMPLETE MARKETS

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### Author and article information

###### Journal
14 June 2011
###### Article
1106.2743
772d35e4-b9eb-4031-b618-7378b1907368