美式回望期权定价的有限元超收敛分析(英文)  

Superconvergence of Finite Element Methods for Pricing Options

作　　者：林群[1] 张书华[2] 

机构地区：[1]中国科学院数学与系统科学研究院,北京100190 [2]天津财经大学数学经济研究中心,天津300222

出　　处：《应用泛函分析学报》2009年第1期20-32,共13页Acta Analysis Functionalis Applicata

基　　金：supported in part by the Special Funds for Major State Basic Research Project (2007CB814906);the National Natural Science Foundation of China (10471019,10471103, and10771158);Social Science Foundation of the Ministry of Education of China (numerical methods for convertiblebonds,06JA630047);Tianjin Natural Science Foundation (07JCYBJC14300);the State Key Laboratory ofScientific and Engineering Computing,and Tianjin University of Finance and Economics

摘　　要：考虑美式回望看跌期权的有限元方法.在把原问题转化成等价的变分不等式的基础上,研究了半离散格式在L2和L∞范数意义下的最优误差估计.此外,为了进一步提高逼近解的精度,借助超收敛分析技术和插值后处理方法,研究了H1范数意义下的整体超收敛以及后验误差估计.We are concerned with finite element methods for pricing American lookback put options. On the basis of converting the problem into the equivalent variational inequality, the semidiscrete scheme is presented, and the L^2- and L^∞- error estimates are established, respectively. In addition, to enhance further the approximation solutions, by means of a superapproximation analysis technique and an interpolation postprocessing method, we study global superconvergence estimates in H^1- norm for linear finite elements. As by-products, the global supereonvergence results can be used to generate a posteriori error estimators.

关 键 词：美式回望期权 变分不等式 有限元方法 最优和超收敛估计 插值后处理 后验误差估计子 

分 类 号：O24[理学—计算数学] F22[理学—数学]