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Explicit Solution of a Non-Linear Filtering Problem for Lévy Processes with Application to Finance

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Abstract

In this paper we explicitly solve a non-linear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by empirical observations of R. Cont and P. Tankov we propose a model for financial assets, which captures the phenomenon of time inhomogeneity of the jump size density. We apply the explicit formula to obtain the optimal filter for the corresponding filtering problem.

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Authors and Affiliations

  1. Centre of Mathematics for Applications (CMA), Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N-0316 Oslo, Norway

    Thilo Meyer-Brandis & Frank Proske

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  1. Thilo Meyer-Brandis
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  2. Frank Proske
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Correspondence to Thilo Meyer-Brandis or Frank Proske.

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Meyer-Brandis, T., Proske, F. Explicit Solution of a Non-Linear Filtering Problem for Lévy Processes with Application to Finance. Appl Math Optim 50, 119–134 (2004). https://doi.org/10.1007/s00245-004-0798-6

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  • DOI: https://doi.org/10.1007/s00245-004-0798-6

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