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Article Dans Une Revue The Annals of Applied Probability Année : 2016

Numerical simulation of quadratic BSDEs

Résumé

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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Dates et versions

hal-00990555 , version 1 (13-05-2014)
hal-00990555 , version 2 (22-09-2014)

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Jean-François Chassagneux, Adrien Richou. Numerical simulation of quadratic BSDEs. The Annals of Applied Probability, 2016, 26 (1), ⟨10.1214/14-AAP1090⟩. ⟨hal-00990555v2⟩

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