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Quantization based filtering method using first order approximation

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TitleQuantization based filtering method using first order approximation
Publication TypeJournal Article
Year of Publication2010
AuthorsAfef Sellami
JournalSIAM journal on numerical analysis
Volume47
Issue6
Pagination4711-4734
Keywordsapproximation order, convergence, discrete time, Filtering, finance, grid pattern, linear approximation, linear model, Monte Carlo method, non linear approximation, numerical analysis, numerical approximation, numerical integration, numerical method, stochastic method, stochastic model
Abstract

The quantization based filtering method (see [1] is a grid based approximation method to solve nonlinear filtering problems with discrete time observations. It relies on off-line preprocessing of some signal grids in order to construct fast recursive schemes for filter approximation. We give here an improvement of this method by taking advantage of the stationary quantizer property. The key ingredient is the use of vanishing correction terms to describe schemes based on piecewise linear approximations. Convergence results are given and numerical results are presented for the particular cases of linear Gaussian model and stochastic volatility models.

References

  1. Gilles Pagès, Huyên Pham, and Jacques Printems, Optimal quantization methods and applications to numerical problems in finance, , 2004.