Numerical simulation of quadratic BSDEs
Provides the first rigorous error analysis and implementable algorithm for quadratic BSDEs, addressing a known bottleneck in numerical methods for these equations.
This paper develops a numerical scheme for quadratic BSDEs with bounded terminal conditions, achieving a time-discretization error of order 1/2 - ε. The method is implemented via quantization and validated with numerical examples.
This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to $z$ and bounded terminal conditions. We first study a slight modification of the classical dynamic programming equation arising from the time-discretization of BSDEs. By using a linearization argument and BMO martingales tools, we obtain a comparison theorem, a priori estimates and stability results for the solution of this scheme. Then we provide a control on the time-discretization error of order $\frac{1}{2}-\varepsilon$ for all $\varepsilon>0$. In the last part, we give a fully implementable algorithm for quadratic BSDEs based on quantization and illustrate our convergence results with numerical examples.