走向现代数学学术报告 - 陈旭副教授（No. 895)

报告题目：Fast solution strategies for time-space fractional linear complementarity problems governing American options pricing

报告时间：2025年12月12日 15:00

报告地点：东海岸校区-D实232

报 告 人：陈旭 副教授（广东工业大学）

邀 请 人：黄云驰 博士

报告摘要：Fractional derivatives are widely used in various fields to model the historical dependence or spatial globalization of the solutions because of their nonlocal properties. In finance, European option pricing models with time-space fractional derivatives have been proposed, and related numerical algorithms have been developed. However, to the best of our knowledge, the American option pricing model and its numerical methods have yet to be studied. In this paper, a linear complementary problem involving time-space fractional derivatives governing American option valuation has been considered. A penalized numerical scheme is developed to discretize the problem with stability and convergence analysis. Further, to reduce the memory requirement caused by the time-fractional derivative, an improved fast numerical scheme based on the sum-of-exponentials approximation has been proposed with stability analysis. A Newton-Krylov subspace method, combining a proposed novel banded preconditioner with the spectrum and condition number guarantee, is used to solve nonlinear schemes efficiently. Numerical experiments, including a real-world example, are present to show the efficiency of the proposed fast solution strategies.

报告人简介：陈旭，男，哲学博士，广东工业大学经济学院副教授。本科毕业于汕头大学数学与应用数学专业（金融方向），博士毕业于澳门大学数学专业（计算数学方向）。主要从事金融衍生品定价算法、分数阶偏微分方程数值解及数值线性代数方法等方面的研究，重点关注分数阶模型、线性/非线性互补问题与高效预处理迭代算法在期权定价与金融工程中的应用。近年来在 Journal of Scientific Computing、Computers & Mathematics with Applications、Numerical Algorithms 等 SCI/EI 检索期刊发表学术论文19篇，主持国家自然科学基金青年项目1项、参与国家自然科学基金面上项目1项，主持省部级科研项目2项，并参与多项省部级及企业合作科研项目。