Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/43770
Authors: 
Herzberg, Frederik
Year of Publication: 
2008
Series/Report no.: 
Working papers // Institute of Mathematical Economics 404
Abstract: 
This article shows that the nonstandard approach to stochastic integration with respect to (C² functions of) Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to (C² functions of) jump-diffusions with finite-variation jump part. It is proven that internal stochastic integrals with respect to hyperfinite Lévy processes possess right standard parts, and that these standard parts coincide with the classical pathwise stochastic integrals, provided the integrator's jump part is of finite variation. If the integrator's Lévy measure is bounded from below, one can obtain a similar result for stochastic integrals with respect to C² functions of Lévy processes. As a by-product, this yields a short, direct nonstandard proof of the generalized Itô formula for stochastic differentials of smooth functions of Lévy processes.
Subjects: 
Lévy processes
Stochastic integration
Nonstandard analysis
Itô formula
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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