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


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.


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Jean-François Chassagneux. Adrien Richou. "Numerical simulation of quadratic BSDEs." Ann. Appl. Probab. 26 (1) 262 - 304, February 2016.


Received: 1 July 2013; Revised: 1 September 2014; Published: February 2016
First available in Project Euclid: 5 January 2016

zbMATH: 1334.60129
MathSciNet: MR3449318
Digital Object Identifier: 10.1214/14-AAP1090

Primary: 60H10 , 65C30

Keywords: Backward stochastic differential equations , Generator of quadratic growth , numerical approximation , time-discretization

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 1 • February 2016
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