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Esscher transforms and the minimal entropy martingale measure for exponential Lévy models. (English) Zbl 1099.60033

In the main result of this paper some previous work on the minimum entropy martingale measure \(\widehat{P}\) for exponential Lévy processes \(S_t = S_0 \exp(X)\) is completed. \(\widehat{P}\) exists if and only if the Esscher martingale measure for the stochastic logarithm \(\widetilde{X}\) of \(S\), i.e. \(S_t = S_0 \, \mathcal{E}(\widetilde{X})_t\), exists and then they are equal. Several examples are discussed.

MSC:

60G44 Martingales with continuous parameter
60G51 Processes with independent increments; Lévy processes

Keywords:

Lévy processes
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