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.
Additional Metadata
Keywords backward stochastic differential equations, Fourier cosine expansion method, European options, market imperfections, jump-diffusion process, utility indifference pricing
THEME Null option (theme 11)
Publisher S.I.A.M.
Persistent URL dx.doi.org/10.1137/130913183
Journal SIAM Journal on Scientific Computing
Citation
Ruijter, M.J, & Oosterlee, C.W. (2015). A Fourier cosine method for an efficient computation of solutions to BSDE. SIAM Journal on Scientific Computing, 37(2), A859–A889. doi:10.1137/130913183