| 期权定价问题的数值方法 |
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| 引用本文： | 刘棠,张盘铭. 期权定价问题的数值方法[J]. 系统科学与数学, 2004, 24(1): 010-016 |
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| 作者姓名： | 刘棠 张盘铭 |
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| 作者单位： | 1. 天津财经学院基础部,天津,300222;南开大学天津大学刘徽应用数学中心,天津,300072
2. 天津财经学院科研处,天津,300222 |
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| 基金项目： | 天津市高等学校科技发展基金，南开大学天津大学刘徽数学中心(021306)项目资助课题 |
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| 摘 要： | 本文研究以股票为标的资产的美式看跌期权定价问题的数值方法,即有限元方法。通过将所考虑的问题转化为等价的变分不等式,并利用积分恒等式与超逼近分析技术,得到了半离散有限元方法的最优L~2-模与L~∞-模的误差估计。
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| 关 键 词： | 美式看跌期权 变分不等式 有限元方法 最优误差估计 |
| 修稿时间： | 2002-11-18 |
NUMERICAL METHODS FOR OPTION PRICING PROBLEMS |
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| Tang LIU,Pan Ming ZHANG. NUMERICAL METHODS FOR OPTION PRICING PROBLEMS[J]. Journal of Systems Science and Mathematical Sciences, 2004, 24(1): 010-016 |
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| Authors: | Tang LIU Pan Ming ZHANG |
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| Affiliation: | (1)Department of Mathematics,Tianjin University of Finance and Economics, Tianjin 300222;Liu Hui Center for Applied Mathematics of Nankai University and Tianjin University, Tianjin 300072;(2)Department of Scientific Research, Tianjin University of Finance and Economics, Tianjin 3 |
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| Abstract: | In this paper we are concerned with numericalapproximations, finite element methods,to the valuation ofAmerican put options on stocks. By reformulating the problem inquestion into a variational inequality and using integralidentities as well as super-close analysis technique, we obtainthe optimal $L^2$-norm and $L^{infty}$-norm estimates for thesemi-discrete finite element scheme. |
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| Keywords: | American put option variational inequality finite element method optimal error estimate. |
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