Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-45

December 2000

We consider construction of Normal Inverse Gaussian (NIG) (and some related) Lévy processes from the probabilistic viewpoint and from the one of the theory of pseudo-differential operators, and then we introduce and analyse natural generalisations of these constructions. The resulting Feller processes are somewhat similar to the NIG Lévy process but may, for instance, possess mean-reverting features. Possible applications to Financial Mathematics are discussed, and approximations to solutions of corresponding generalisations of Black-Scholes equation are derived.

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