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SECOND-ORDER NUMERICAL SCHEMES FOR DECOUPLED FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS
  • ISSN号：0254-9409
  • 期刊名称：《计算数学：英文版》
  • 时间：0
  • 分类：O[理学]
  • 作者机构：[1]Department of Mathematics, Shandong University, Jinan, Shandong 250100, China, [2]Department of Mathematics, Beijing University of Technology, Beijing 100022, China, [3]Department of Computational and Applied Mathematics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
  • 相关基金：The authors would like to thank the referees for their valuable comments, which improved much of the quality of the paper. This work is partially support- ed by the National Natural Science Foundations of China under grant numbers 91130003,11171189 and 11571206; by Natural Science Foundation of Shandong Province under grant number ZR2011AZ002; by the U.S. Department of Energy, Office of Science, Office of Ad- vanced Scientific Computing Research, Applied Mathematics program under contract number ERKJE45; and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT-Battelle, LLC, for the U.S. Department of Energy under Contract DE-AC05-00OR22725.
作者： Weidong Zhao[1], Wei Zhang[2], Guannan Zhang[3]
关键词： 提交向后算法, 随机的微分方程, BROWNIAN, 运动, 随机的措施, 分离时间的系统, 近似理论, Decoupled FBSDEs with Lévy jumps, Backward Kolmogorov equation, Non-linear Feynman-Kac formula, Second-order convergence, Error estimates.
中文摘要：

我们为 decoupled 提交向后建议新数字计划随机的微分方程(FBSDE ) 与跳，在随机的动力学被一个 ddimensional Brownian 运动和独立补偿泊松随机驾驶的地方，测量。一个半分离的计划为分离时间近似被开发，它被一个经典计划为前面的 SDE 组成

英文摘要：

We propose new numerical schemes for decoupled forward-backward stochastic differ- ential equations （FBSDEs） with jumps, where the stochastic dynamics are driven by a d- dimensional Brownian motion and an independent compensated Poisson random measure. A semi-discrete scheme is developed for discrete time approximation, which is constituted by a classic scheme for the forward SDE [20, 28] and a novel scheme for the backward SDE. Under some reasonable regularity conditions, we prove that the semi-discrete scheme can achieve second-order convergence in approximating the FBSDEs of interest; and such convergence rate does not require jump-adapted temporal discretization. Next, to add in spatial discretization, a fully discrete scheme is developed by designing accurate quadrature rules for estimating the involved conditional mathematical expectations. Several numerical examples are given to illustrate the effectiveness and the high accuracy of the proposed schemes.

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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
  • 邮箱：
  • 电话：
  • 国际标准刊号：ISSN：0254-9409
  • 国内统一刊号：ISSN：11-2126/O1
  • 邮发代号:
  • 获奖情况:
  • 中国期刊方阵“双效”期刊
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国科学引文索引（扩展库）,英国科学文摘数据库,日本日本科学技术振兴机构数据库
  • 被引量:193