DISCRETE-TIME APPROXIMATION OF MULTIDIMENSIONAL BSDES WITH OBLIQUE REFLECTIONS

• 成果类型: Article
• 署名作者: Chassagneux, Jean-Francois; Elie, Romuald; Kharroubi, Idris
• 署名单位: Universite Paris Saclay; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP771
• 发表日期: 2012
• 页码: 971-1007
• 关键词: pdes

摘要

In this paper, we study the discrete-time approximation of multidimensional reflected BSDEs of the type of those presented by Hu and Tang [Probab. Theory Related Fields 147 (2010) 89-121] and generalized by Hamadene and Zhang [Stochastic Process. Appl. 120 (2010) 403-426]. In comparison to the penalizing approach followed by Hamadene and Jeanblanc [Math. Oper Res. 32 (2007) 182-192] or Elie and Kharroubi [Statist. Probab. Lett. 80 (2010) 1388-1396], we study a more natural scheme based on oblique projections. We provide a control on the error of the algorithm by introducing and studying the notion of multidimensional discretely reflected BSDE. In the particular case where the driver does not depend on the variable Z, the error on the grid points is of order 1/2 - epsilon, epsilon > 0.