一种新型美式期权的自由边界问题

基金项目:

国家青年科学基金;广东省自然科学基金

详细信息

Free boundary problem of a new type of American Option

摘要: 研究一种新类型的股票期权定价问题, 此类期权是当股票市场不利于普通的美式股票期权的时候, 提供了一个最低保障.将该金融问题转化为一个具有2条自由边界的抛物变分不等式,利用偏微分方程理论证明了该问题解的存在唯一性,并且得到2条自由边界的存在性、单调性和光滑性, 以及抛物变分不等式的解与最低保障之间的关系.
- 自由边界.
Abstract: A parabolic variational inequality with two free boundaries arising from a new type of stock option pricing is considered, which provides a guaranteed minimum as an added incentive in case the market appreciation of the stock is low. The existence and uniqueness of solution to the problem via the PDE technique are proved. Moreover, the existence, monotonicity and smoothness of two free boundaries, and the relationship between the solution to the parabolic variational inequality and the guaranteed minimum are obtained.
- free boundary