A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs

Ruijter, M.J.; Oosterlee, C.W.

A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs

Journal article (2015)

Authors

M.J. Ruijter

C.W. Oosterlee

Department

Delft Institute of Applied Mathematics () (TU Delft)

Backward stochastic differential equations European options Fourier cosine expansion method Market imperfections Jump-diffusion process Utility indifference pricing

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Published Date

16-04-2015

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Source:

SIAM Journal on Scientific Computing, 37 (2), 2015

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Abstract

We develop a Fourier method to solve backward stochastic differential equations (BSDEs). A general theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier cosine series expansions, relying on the availability of a characteristic function. The method is applied to BSDEs with jumps. Numerical experiments demonstrate the applicability of BSDEs in financial and economic problems and show fast convergence of our efficient probabilistic numerical method.

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