We are interested in a nonlinear filtering problem motivated by an
information-based approach for modelling the dynamic evolution of a
portfolio of credit risky securities.
We solve this
problem by `change of measure method\\\' and show the existence of the
density of the unnormalized conditional distribution which is a
solution to the Zakai equation. Zakai equation is a linear SPDE
which, in general, cannot be solved analytically. We apply Galerkin
method to solve it numerically and show the convergence of Galerkin
approximation in mean square. Lastly, we design an adaptive Galerkin
filter with a basis of Hermite polynomials and we present numerical
examples to illustrate the effectiveness of the proposed method. The
work is closely related to the paper Frey and Schmidt (2010).
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-65103 |
| Date | 16 February 2011 |
| Creators | Xu, Ling |
| Contributors | Ling Xu, Fakultät für Mathematik und Informatik., Professor Rüdiger Frey, Professor Thorsten Schmidt |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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