Some Non-monotone Schemes for Time Dependent Hamilton–Jacobi–Bellman Equations in Stochastic Control

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• 作者：Xavier Warin
• 关键词：Hamilton–Jacobi–Bellman equations ; Stochastic control ; Numerical methods ; Semi ; Lagrangian ; 49L20 ; 65N12
• 刊名：Journal of Scientific Computing
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：66
• 期：3
• 页码：1122-1147
• 全文大小：597 KB
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• 作者单位：Xavier Warin (1)
  
  1. EDF R&D, FiME, Laboratoire de Finance des Marchés de l’Energie, Clamart, France
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691

文摘

We introduce some approximation schemes for linear and fully non-linear diffusion equations of Bellman type. Based on modified high order interpolators, the schemes proposed are not monotone but one can prove their convergence to the viscosity solution of the problem. Some of these schemes are related to a scheme previously proposed without proof of convergence. Effective implementation of these schemes in a parallel framework is discussed. They are extensively tested on some simple test case, and on some difficult ones where theoretical results of convergence are not available. Keywords Hamilton–Jacobi–Bellman equations Stochastic control Numerical methods Semi-Lagrangian