定价问题和一类倒向随机微分方程解的存在唯一性  

Pricing Problem and Existance/Uniqueness of Backward Stochastic Differential Equations

作　　者：孙志强 

机构地区：[1]复区大学管理学院,上海200433

出　　处：《应用概率统计》1998年第4期409-418,共10页Chinese Journal of Applied Probability and Statistics

摘　　要：本文建立了由一个多维Brown运动、Poisson过程和跳时固定的简单点过程共同驱动的股票价格模型．在此模型下，将未定权益的定价问题归结为一类倒向随机微分方程的求解问题．证明了这类倒向随机微分方程适应解的存在唯一性问题，并给出了一个关于未定权益的定价公式．In this paper, the option pricing problem in a complete financial market containing a bond and a finite number of stocks whose prices are driven by a multidimensional Brownian motion process, a multidimensional Poisson point process and a multidimensional Step point process is set. Under the frame of this market, we reduce the pricing problem to solution problem of a backward stochastic differential equation(BSDE). Moreover, the existence and uniqueness of the solution of this BSDE are proven.

关 键 词：随机微分方程 解 定价问题 BSDE 股票价格模型 

分 类 号：F830.9[经济管理—金融学] O211.63[理学—概率论与数理统计]