数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1721-1729.doi: 10.1016/S0252-9602(10)60165-8

• 论文 • 上一篇    下一篇

THE REGULARITY OF THE FREE BOUNDARY FOR |STRIKE RESET OPTION

 杨舟   

  1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2007-11-30 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    The project is supported by National Natural Science Foundation of China (10901060, 10971073, 1081056), and Natural Science Foundation of Guangdong Province (9451063101002091).

THE REGULARITY OF THE FREE BOUNDARY FOR |STRIKE RESET OPTION

 YANG Zhou   

  1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • Received:2007-11-30 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    The project is supported by National Natural Science Foundation of China (10901060, 10971073, 1081056), and Natural Science Foundation of Guangdong Province (9451063101002091).

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摘要：

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was  showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.

关键词: strike reset option, free boundary, variational inequality, the comparison principle

Abstract:

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a parabolic variational inequality and the optimal reset strategy is the free boundary. The smoothness of the free boundary in some cases was  showed in our article published in JDE. We would prove its smoothness in the other case in this paper by a generalized comparison principle for the variational inequality.

Key words: strike reset option, free boundary, variational inequality, the comparison principle

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