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

Meyer-Brandis, Thilo und Proske, Frank (2004): Explicit Solution of a Non-Linear Filtering Problem for Lévy Processes with Application to Finance. In: Applied Mathematics and Optimization, Bd. 50, Nr. 2: S. 119-134

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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0095-4616
• Sprache: Englisch