Lévy processes martingale measures relative entropy f-divergences minimal entropy martingale measure Eshscer martingale transform mathematical finance incomplete markets Minimal Entropy Martingale Measure for Lévy Processes Katja Krol Krol Katja Uwe Küchler Küchler Uwe Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

Minimal Entropy Martingale Measure for Lévy Processes

Katja Krol , Uwe Küchler

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

60G51 Processes with independent increments
91B28 Finance, portfolios, investment

Abstract
Let X be a real-valued Lévy process under P in its natural filtration. The minimal entropy martingale measure is defined as an absolutely continuous martingale measure that minimizes the relative entropy with respect to P. We show in this paper that the sufficient conditions for its existence, known in literature, are also necessary and give an explicit formula for the infimum of the relative entropy.

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