[1]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.[doi:10.3969/j.issn.1000-5013.2006.02.006]
　Wang Zhihuan.Critical Analysis for the Solution of Free Doundary Problem[J].Journal of Huaqiao University(Natural Science),2006,27(2):133-136.[doi:10.3969/j.issn.1000-5013.2006.02.006]
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一类自由边界问题解的渐近性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第27卷
期数:
2006年第2期
页码:
133-136
栏目:
出版日期:
2006-04-20

文章信息/Info

Title:
Critical Analysis for the Solution of Free Doundary Problem
文章编号:
1000-5013(2006)02-0133-04
作者:
王志焕
华侨大学数学系 福建 泉州 362021
Author(s):
Wang Zhihuan
Department of Mathematics, Huaqiao University, 362021, Quanzhou, China
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
Keywords:
jump-diffusion model;  parabolic integro-differential equation;  free boundary problem;  convergence property
分类号:
O175.26
DOI:
10.3969/j.issn.1000-5013.2006.02.006
文献标志码:
A
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.
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.

参考文献/References:

[1] Merton R C. Option pricing when underlying stock returns are discontinuous [J]. Journal of Financial Economics, 1976(3):125-144.doi:10.1016/0304-405X(76)90022-2.
[2] Willmott P. Derivatives:The theory and practice of financial engineering [M]. London:John Wiley & Sons Ltd, 1999.325-337.
[3] Friedman A. 抛物型偏微分方程 [M]. 北京:科学出版社, 1984.186-223.
[4] Phan H. Optmal stopping, free boundary and Amertcan optlon in a jumpdiffusion model [J]. Applied Mathematics and Optimization, 1996.145-164.
[5] 代晓亮, 边保军, 袁桂秋. 美式期权当执行日期趋于无穷大时的渐近分析 [J]. 同济大学学报(自然科学版), 2005(4):545-549.doi:10.3321/j.issn:0253-374X.2005.04.025.

备注/Memo

备注/Memo:
国务院侨务办公室科研基金资助项目(03QZR9)
更新日期/Last Update: 2014-03-23