Linear hyperfinite Lévy integrals

Frederik Herzberg

No 404, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: This article shows that the nonstandard approach to stochastic integration with respect to (C^2 functions of) Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to (C^2 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 C^2 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.

Keywords: Itô formula; Nonstandard analysis; Lévy processes; Stochastic integration (search for similar items in EconPapers)
Date: 2011-08-15
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (2)

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