## 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

Lévy processes
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### References:

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