NUMERICAL SIMULATION OF QUADRATIC BSDES

• 成果类型: Article
• 署名作者: Chassagneux, Jean-Francois; Richou, Adrien
• 署名单位: Imperial College London; Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux; CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1090
• 发表日期: 2016
• 页码: 262-304
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; Utility maximization; convex generators; approximation; CONVERGENCE; uniqueness; EXISTENCE; algorithm; schemes; drivers

摘要

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 1/2 - epsilon for all epsilon > 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.