源于俄式期权定价的自由边界问题  

A Free Boundary Problem Arising from the Valuation of the Russian Option

作　　者：易法槐[1] 余涛[2] 

机构地区：[1]华南师范大学数学科学学院,广州510631 [2]中国科学技术大学数学系,合肥230026

出　　处：《应用数学学报》2008年第6期993-1012,共20页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.10671075);广东省自然科学基金(No.5005930);高等学校博士学科点专项科研基金(20060574002)资助项目

摘　　要：本文主要应用PDE方法对俄式期权定价问题进行理论分析.类似于美式期权定价问题,俄罗斯期权定价问题可归结为一个一维抛物型变分不等式.我们首先引入惩罚函数证明了该变分不等式的解的存在唯一性,然后研究了自由边界的一些性质,如单调性、光滑性和自由边界的位置.In this paper we use a PDE argument to deal with the theoretical analysis of the valuation of the Russian option. As the valuation of the American option, the valuation of the Russian options can be formulated as a one-dimensional parabolic variational inequality. First we introduce a penalty function and prove the existence and uniqueness of the solution of the variational inequality. Then we study the properties of the free boundary, such as monotonicity, smoothness and the location of the free boundary.

关 键 词：俄罗斯期权 期权定价 变分不等式 自由边界 

分 类 号：O175.29[理学—数学]