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On the Fourier cosine series expansion method for stochastic control problems
Author(s) -
Ruijter M.J.,
Oosterlee C.W.,
Aalbers R.F.T.
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1866
Subject(s) - sine and cosine transforms , algorithm , toeplitz matrix , mathematics , fourier series , trigonometric functions , computation , series (stratigraphy) , fourier transform , extrapolation , discrete cosine transform , frequency domain , discrete fourier transform (general) , discrete fourier series , mathematical optimization , computer science , fourier analysis , mathematical analysis , fractional fourier transform , paleontology , geometry , artificial intelligence , pure mathematics , image (mathematics) , biology
SUMMARY We develop a method for solving stochastic control problems under one‐dimensional Lévy processes. The method is based on the dynamic programming principle and a Fourier cosine expansion method. Local errors in the vicinity of the domain boundaries may disrupt the algorithm. For efficient computation of matrix–vector products with Hankel and Toeplitz structures, we use a fast Fourier transform algorithm. An extensive error analysis provides new insights based on which we develop an extrapolation method to deal with the propagation of local errors. Copyright © 2013 John Wiley & Sons, Ltd.
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