作　　者： (陈晓珊）; (曹利敏）; (易法槐）;

机构地区： 华南师范大学数学科学学院,广州510631

出　　处： 《华南师范大学学报（自然科学版）》 2017年第4期95-101,共7页

摘　　要： 研究一种新类型的股票期权定价问题,当股票市场不利于普通的美式股票期权时,此类期权为持有者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. 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.

关 键 词： 期权定价 变分不等式 自由边界