跳扩散路径依赖期权在固定比例交易费用下的计算  

THE COMPUTATION ON THE PATH DEPENDENT OPTION WITH JUMP DIFFUSION UNDER FIXED TRADE COST RATE

作　　者：吴强[1] 张寄洲[2] 

机构地区：[1]同济大学应用数学系,上海200092 [2]上海师范大学数理学院,上海200234

出　　处：《华南师范大学学报（自然科学版）》2009年第2期24-28,43,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：国家重点基础研究发展计划(973计划)资助课题(2007CB814903);国家自然科学基金资助项目(10671144);上海市科委重大科技攻关资助项目(075105118)}

摘　　要：考虑了市场存在交易费用下的跳扩散路径依赖期权的定价问题,将该问题转化为两元的随机控制问题.给出了股票价格服从跳扩散下的价值函数对应的积分微分不等方程,并通过马氏链对变分问题进行离散,证明了离散形式是变分不等式的约束粘性解.A problem of pricing jump - diffusion path - dependent option is considered in the market with transaction costs. The problem is transformed to a stochastic control problem with two control variables. Integral - differential inequality in corresponding with the value function which the stock price follows jump - diffusion is given. Based on the Markov chain to the discrete form, it is shown that the discrete form is the constraint viscosity solution of the variational inequality.

关 键 词：效用最大化 路径依赖 跳扩散 马尔科夫链 约束粘性解 随机控制 

分 类 号：O29[理学—应用数学]