On the Fourier cosine series expansion method for stochastic control problems

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.