The Annals of Applied Probability

Numerical simulation of quadratic BSDEs

Jean-François Chassagneux and Adrien Richou

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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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 1 (2016), 262-304.

Dates
Received: July 2013
Revised: September 2014
First available in Project Euclid: 5 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1452003239

Digital Object Identifier
doi:10.1214/14-AAP1090

Mathematical Reviews number (MathSciNet)
MR3449318

Zentralblatt MATH identifier
1334.60129

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 65C30: Stochastic differential and integral equations

Keywords
Backward stochastic differential equations generator of quadratic growth time-discretization numerical approximation

Citation

Chassagneux, Jean-François; Richou, Adrien. Numerical simulation of quadratic BSDEs. Ann. Appl. Probab. 26 (2016), no. 1, 262--304. doi:10.1214/14-AAP1090. https://projecteuclid.org/euclid.aoap/1452003239


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