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Tempered stable distributions and processes. (English) Zbl 1352.60021
The tempered stable distributions are perturbations of stable distributions obtained by adding an exponential weight on the jumping density, which allows for finite variance. It can also be viewed as a generalization of bilateral Gamma and CGMY distributions, which appear as weak limits. In this paper, the authors gather several simple analytical observations on the tempered stable distributions. They also consider the equivalent martingale measure transformations preserving the class of the associated tempered stable processes, in the framework of exponential stock prices models. In contrast to bilateral Gamma stock models, it may happen that there is no such martingale measure.

##### MSC:
 60E07 Infinitely divisible distributions; stable distributions 60G51 Processes with independent increments; Lévy processes 91G20 Derivative securities (option pricing, hedging, etc.)
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