| 一类自由边界问题解的渐近性 |
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| 引用本文： | 王志焕.一类自由边界问题解的渐近性[J].华侨大学学报(自然科学版),2006,27(2):133-136. |
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| 作者姓名： | 王志焕 |
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| 作者单位： | 华侨大学数学系,福建,泉州,362021 |
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| 基金项目： | 国务院侨务办公室科研基金资助项目(03QZR9) |
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| 摘 要： | 讨论一类抛物积微分方程自由边界问题解的渐近性．利用偏微分方程的渐近性理论,证明在无界区域上一类抛物积微分方程自由边界问题的解,以及当时间趋于无穷大时,收敛于稳态的积微分方程自由边界问题的解．这一结论可用于解释期权定价中带跳扩散模型,当执行日期趋于无穷大时,美式期权价格及最佳实施边界收敛于永久美式期权价格及最佳实施边界．
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| 关 键 词： | 跳扩散模型 抛物积微分方程 自由边界问题 收敛性 美式期权 定价模型 |
| 文章编号： | 1000-5013（2006）02-0133-04 |
| 收稿时间： | 2005-10-03 |
| 修稿时间： | 2005-10-03 |
Critical Analysis for the Solution of Free Doundary Problem |
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| Wang Zhihuan.Critical Analysis for the Solution of Free Doundary Problem[J].Journal of Huaqiao University(Natural Science),2006,27(2):133-136. |
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| Authors: | Wang Zhihuan |
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| Institution: | Department of Mathematics, Huaqiao University, 362021, Quanzhou, China |
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| Abstract: | The intent of this study is to discuss the critical property of a free boundary problem of a parabolic integro-dif-ferential equation. Using the critical theory of partial differential equation, we prove that the solution of a free boundary problem of parabolic integro-differential equation converges to the solution of a free boundary problem of integro-differen-tial equation in limitless region when time run to infinite. Using this result, we can explain that the price and optimal exercise boundary of American option converge to the price and optimal exercise boundary of perpetual American option when the expiry date runs to infinite in a jump-diffusion model. |
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| Keywords: | jump-diffusion model parabolic integro-differential equation free boundary problem convergence property |
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