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 \({f}^{{\prime\prime}}(x)\,=\,a{x}^{\gamma },\,a > 0,\,\gamma \in \mathbb{R}\), we give necessary and sufficient conditions for existence of f-minimal martingale measure.
Mathematics Subject Classification (2010): 60G07, 60G51, 91B24
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Acknowledgements
This work is supported in part by ECOS project M07M01 and by ANR-09-BLAN-0084-01 of the Department of Mathematics of Angers’s University.
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Cawston, S., Vostrikova, L. (2013). Levy Preservation and Associated Properties for f -Divergence Minimal Equivalent Martingale Measures. In: Shiryaev, A., Varadhan, S., Presman, E. (eds) Prokhorov and Contemporary Probability Theory. Springer Proceedings in Mathematics & Statistics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33549-5_9
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DOI: https://doi.org/10.1007/978-3-642-33549-5_9
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