Abstract
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.
Citation
Jean-François Chassagneux. Adrien Richou. "Numerical simulation of quadratic BSDEs." Ann. Appl. Probab. 26 (1) 262 - 304, February 2016. https://doi.org/10.1214/14-AAP1090
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