学术报告

题      目：A High-Order Numerical Method for BSPDEs with Applications to Mathematical Finance

报  告  人：李运章  副研究员  (邀请人：杨舟 )

                                   复旦大学

时      间：1月8日  14：00-15：00

地     点：数科院西楼二楼会议室

报告人简介:

        李运章，复旦大学智能复杂体系实验室青年副研究员。主要研究领域为随机系统的最优控制问题的高阶精度数值算法，相关成果发表于SIAM J. Control. Optim., SIAM J. Sci. Comput., SIAM J. Financial Math., ESAIM: M2AN等知名学术期刊。入选上海市晨光计划，国家博士后创新人才支持计划，上海市“超级博士后”激励计划。主持国家自然科学基金委青年科学基金项目，上海市“科技创新行动计划”基础研究领域项目，中国博士后科学基金面上项目，获得复旦大学新工科人才基金资助。

摘      要：

       In this paper, we propose a local discontinuous Galerkin (LDG) method for backward stochastic partial differential equations (BSPDEs), which is a high-order numerical scheme. We prove the L2-stability of the numerical scheme. For the super-parabolic BSPDEs, the optimal error estimates are obtained for Cartesian meshes with Q^k elements, and the sub-optimal error estimates are derived for triangular meshes with P^k elements. We also prove the suboptimal error estimates for the degenerate BSPDEs. Numerical examples in one and two space dimensions are given to display the performance of the LDG method. As an application in mathematical finance, the numerical scheme is applied to approximate the hedging price of a contingent claim and the corresponding optimal hedging strategy.

        欢迎老师、同学们参加、交流！