CHASSAGNEUX, Jean-François; RICHOU, Adrien

doi:10.1214/14-AAP1090

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CHASSAGNEUX, Jean-François
Department of Mathematics [Imperial College London]

RICHOU, Adrien
Institut de Mathématiques de Bordeaux [IMB]

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The Annals of Applied Probability. 2016, vol. 26, n° 1

Institute of Mathematical Statistics (IMS)

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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.< Leer menos