Numerical simulation of quadratic BSDEs - Archive ouverte HAL Access content directly
Journal Articles Annals of Applied Probability Year : 2016

Numerical simulation of quadratic BSDEs

(1) , (2)
1
2

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.
Fichier principal
Vignette du fichier
CR13_rev1.pdf (692.47 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

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

Identifiers

Cite

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

Collections

CNRS INSMI ANR
152 View
152 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More