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Consider $X= \left( X_t \right)_{t\geq 0}$ is a Lévy process whose characteristic triplet is $\left( \gamma, \sigma ^2, \nu \right)$ and where its Lévy measure is $$ \nu \left( dx\right) = A \sum_{n=1} ^{\infty} p^n \delta_{-n}\left( dx \right) + Bx^{\beta-1}\left( 1+x \right)^{-\alpha -\beta}e^{-\lambda x } \mathbf{1}_{\left ]0,+\infty \right[}\left( x\right)dx.$$

I'd like to know how to show that a price process $S_t = S_0 \exp\left( r t + X_t \right)$ of a risky actif under interest rate $r >0$ is well defined and admits first and second order moments.

Someone could help on it, please?

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closed as not a real question by chrisaycock Feb 24 '13 at 23:51

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

This question was cross-posted here and here, where it has been answered. I'm going to close the question on Quant.SE. – chrisaycock Feb 24 '13 at 23:50