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A sparse-grid method for multi-dimensional backward stochastic differential equations
  • ISSN号：0254-9409
  • 期刊名称：Journal of Computational Mathematics
  • 时间：2013.5.1
  • 页码：221-248
  • 分类：O211.63[理学—概率论与数理统计;理学—数学] O348[理学—固体力学;理学—力学]
  • 作者机构：[1]Department of Scientific Computing, Florida State University, Tallahassee, FL 32306,Computer Science and Mathematics Division, Oak Ridge National Lab, Oak Ridge, TN 37831, [2]Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, [3]School of Mathematics, Shandong University, Jinan, Shandong 250100, China
  • 相关基金：Acknowledgments. The first author was supported by the US Air Force Office of Scientific Research under grant FA9550-11-1-0149. The first author was also supported by the Advanced Simulation Computing Research （ASCR）, Department of Energy, through the Householder Fellowship at ORNL. The ORNL is operated by UT-Battelle, LLC, for the United States Depart-ment of Energy under Contract DE-AC05-00OR22725. The second author was supported by the US Air Force Office of Scientific Research under grant FA9550-11-1-0149. The third author was supported by the Natural Science Foundation of China under grant 11171189. The third author was also supported by the Natural Science Foundation of China under grant 91130003. The thrid author was also supported by Shandong Province Natural Science Foundation under grant ZR2001AZ002.
  • 相关项目：金融数学-金融风险控制中的G-风险度量、倒向随机分析与计算
作者： Guannan Zhang|Max Gunzburger|Weidong Zhao|
关键词： 倒向随机微分方程, 网格法, 多维, 稀疏, 网格方法, 时间离散, BSDE, 数学期望, Backward stochastic differential equations, Multi-step scheme, Gauss-Hermite quadrature rule, Adaptive hierarchical basis, Sparse grids.
中文摘要：

为基于一个多步时间 discretization 计划解决多维的向后的随机的微分方程(BSDE ) 的一个稀少格子的方法[31 ] 被介绍。在多维的空间域，即 Brownian 空间，从原来的方程导出的有条件的数学期望用稀少格子的 Gauss-Hermite 照统治被接近并且(适应) 层次稀少格子的插值。错误估计与简化发电机功能的某些类型为多维的 BSDE 为建议充分分离的计划被证明。最后，几个数字例子被提供说明我们的计划的精确性和效率。[从作者抽象]

英文摘要：

A sparse-grid method for solving multi-dimensional backward stochastic differential equations （BSDEs） based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathe- matical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and （adaptive） hierarchical sparse-grid interpolation. Error estimates are proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Finally, several numerical examples are provided to illustrate the accuracy and efficiency of our scheme.

同期刊论文项目
金融数学-金融风险控制中的G-风险度量、倒向随机分析与计算
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随机微分方程高性能数值算法理论与应用
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期刊信息
  • 《计算数学：英文版》
  • 主管单位:
  • 主办单位:中国科学院数学与系统科学研究院
  • 主编：
  • 地址：北京2719信箱
  • 邮编：100080
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  • 国际标准刊号：ISSN：0254-9409
  • 国内统一刊号：ISSN：11-2126/O1
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  • 中国期刊方阵“双效”期刊
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  • 被引量:193