On the wavelets-based SWIFT method for backward stochastic differential equations
This work provides a more accurate and simpler numerical method for solving backward stochastic differential equations, which are important in mathematical finance and stochastic control.
The paper proposes a wavelet-based SWIFT method for solving backward stochastic differential equations, combining Fourier-based effectiveness with wavelet simplicity, and uses an antireflective boundary technique to reduce boundary errors. Numerical experiments demonstrate improved accuracy and ease of implementation.
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate the problem of errors near the computation boundaries by means of an antireflective boundary technique, giving an improved approximation. We test our algorithm with different numerical experiments.