| 美式回望期权定价的有限元超收敛分析 |
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| 引用本文： | 林群,张书华. 美式回望期权定价的有限元超收敛分析[J]. 应用泛函分析学报, 2009, 11(1): 20-32 |
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| 作者姓名： | 林群 张书华 |
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| 作者单位： | 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 |
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| 基金项目： | 国家重点基础研究发展规划(973计划)，国家自然科学基金，Social Science Foundation of the Ministry of Education of China，天津市自然科学基金，the State Key Laboratory of Scientific and Engineering Computing |
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| 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L^2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H^1范数意义下的整体超收敛以及后验误差估计。
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| 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 |
Superconvergence of Finite Element Methods for Pricing Options |
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| LIN Qan,ZHANG Shu-hua. Superconvergence of Finite Element Methods for Pricing Options[J]. Acta Analysis Functionalis Applicata, 2009, 11(1): 20-32 |
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| Authors: | LIN Qan ZHANG Shu-hua |
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| Affiliation: | 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; 2. Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China) |
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| Abstract: | 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 L2-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 H1-norm for linear finite elements.As by-products,the global superconvergence results can be used to generate a posteriori error estimators. |
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| Keywords: | american lookback options variational inequality finite element methods optimal and superconvergent estimates interpolation postprocessing a posteriori error estimators |
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