Articlegreen2015

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

80 citations0/0 files storedSIAM Journal on Scientific Computing

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Stochastic processes and financial applications Numerical methods for differential equations Fuzzy Systems and Optimization

Abstract

We develop a Fourier method to solve backward stochastic differential equations (BSDEs). 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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References

1973The Pricing of Options and Corporate Liabilities 1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2009Continuous-time Stochastic Control and Optimization with Financial Applications 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations 2000Backward stochastic differential equations and partial differential equations with quadratic growth 2008A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions 1995Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market

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2020Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks 2017Efficient spectral sparse grid approximations for solving multi-dimensional forward backward SDEs 2014Numerical Fourier Method and Second-Order Taylor Scheme for Backward SDEs in Finance 2023Numerical methods for backward stochastic differential equations: A survey

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