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arXiv · 0807.1289

Holomorphic transforms with application to affine processes

D. Belomestny·J. Kampen·J. Schoenmakers
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Abstract

In a rather general setting of Itô-Lévy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transforms into a strip which contains the positive real axis. Based on these extensions we develop a functional series expansion of these transforms in terms of the constituents of the generator. As application, we show that for multidimensional affine Itô-Lévy processes with state dependent jump part the Fourier transform is holomorphic in a time strip under some stationarity conditions, and give log-affine series representations for the transform.

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D. Belomestny, J. Kampen, J. Schoenmakers. 2008-07-08. Holomorphic transforms with application to affine processes. https://arxiv.org/abs/0807.1289

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