讲座:An interior penalty method for finite-dimensional complementarity problems in Financial Engineering

发布时间:2024-06-17浏览次数:10

讲座题目

An interior penalty method for finite-dimensional complementarity problems in Financial Engineering

主办单位

数理与统计学院

协办单位

应用统计

讲座时间

62209:00-10:00

主讲人

Song Wang (汪崧)

讲座地点

行政楼1308

主讲人简介

Song Wang(汪崧)教授,澳大利亚科廷大学Curtin University数学与统计系教授。1982年在武汉大学获得学士学位,1989年在爱尔兰都柏林圣三一学院(Trinity College Dublin)获得博士学位,曾在爱尔兰都柏林的高科技公司--Tritech有限公司工作,先后任澳大利亚新南威尔士大学,科廷科技大学和西澳大利亚大学教授。主要从事偏微分方程的数值解,数值优化和最优控制,金融衍生品定价模型的理论和数值算法等研究。在SIAM  Journal of Optimization, SIAM Journal of Numerical Analysis, Numerische  Mathmatik, Automatica, IEEE Transactions on Neural Networks, IMA  Journal of Numerical Analysis, Reports on Progress in Physics, Journal  of Computational Physics, Biomaterial, Journal of Optimization Theory  and Applications, Journal of Global Optimization等国际SCI知名杂志上发表学术论文150余篇。同时,汪教授还担任多个国际知名SCI杂志的主编,副主编以及编委。

讲座内容简介

In this work we propose and analyse an interior-point based penalty method for a finite-dimensional  large-scale linear and nonlinear complementarity problem (CP) arising  from the discretization of an infinite-dimensional obstacle problem in  classic and financial engineering.  In  this approach, we approximate the CP by a nonlinear algebraic equation  containing a penalty/barrier term with a penalty parameter mu.  The penalty equation is shown to be uniquely solvable. We also prove that the approximate solutions converge to the exact one. A smooth  Newton method is proposed for solving the penalty equation and it is  shown that the linearized system is reducible to two decoupled  subsystems.  Extensions of this method to other types of CPs are will  also be presented. Numerical  experimental results using some non-trivial test problems will be  presented to demonstrate the rates of convergence and accuracy of our  methods.

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