Momentum-Space Approach to Asymptotic Expansion for Stochastic Filtering

Masaaki Fujii
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Masaaki Fujii: The University of Tokyo

No CARF-F-311, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distribution. Thanks to the simplicity of the ODE system, higher order calculation can be performed easily. Furthermore, solving ODEs sequentially with small sub-periods with updated initial conditions makes it possible to implement a substepping method for asymptotic expansion in a numerically efficient way. This is found to improve the performance significantly where otherwise the approximation fails badly. The method is expected to provide a useful tool for more realistic financial modeling with unobserved parameters, and also for problems involving nonlinear measure-valued processes.

Pages: 25 pages
Date: 2012-09, Revised 2013-03
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf311

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