A parabolic variational inequality arising from the valuation of strike reset options

被引：10
作者：
Yang, Zhou
Yi, Fahuai [1 ]
Dai, Min
机构：
[1] S China Nornal Univ, Dept Math, Guangzhou 510631, Guangdong, Peoples R China
[2] Natl Univ Singapore, Dept Math, Singapore 117548, Singapore
[3] Peking Univ, Dept Financial Math, Beijing 100871, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2006年 / 230卷 / 02期
基金：
中国国家自然科学基金;
关键词：
option pricing; strike reset option; free boundary; variational inequality; American option;
D O I：
10.1016/j.jde.2006.07.026
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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 one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C-infinity smoothness of the free boundary are proven in some situations. (c) 2006 Elsevier Inc. All rights reserved.
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页码：481 / 501
页数：21
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