非线性跳跃扩散型多证券价格过程欧式未定权益定价的Black-Scholes方程  

Black-Scholes Equation of European Contingent Claims about Several Securities Whose Prices Are Derived by Nonlinear Jump-diffusion Processes

作　　者：林建忠[1] 叶中行[1] 

机构地区：[1]上海交通大学应用数学系和现代金融研究中心,上海200030

出　　处：《东华大学学报（自然科学版）》2001年第3期32-37,共6页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金重大项目"金融数学;金融工程;金融管理"(79790130)资助

摘　　要：仅讨论一种类型的证券市场模型,其d种股票的价格过程满足一特殊的跳跃扩散型随机微分方程组,即市场风险源的个数与市场风险证券的个数相同。这里首先证明了这一模型下联系于财富过程的跳跃扩散型正倒向随机微分方程组适应解的存在唯一性,由此获得了联系于跳跃扩散型多股票价格过程欧式未定权益的条件期望定价公式,最后利用文献[9]获得的推广线性二阶抛物型方程Cauchy问题解的Feynman-Kac定理导出了欧式未定权益所满足的Black-Scholes方程。This paper deals exclusively with a type of security market model in which the prices of d securities are derived by a m-dimensional Brownian motion and a l-dimentional Poisson process and d - m + I. The existence and uniqueness of the adapted solutions with respect to the jump-diffusion backward stochastic differential equations are proved, the fundamental valuation formula of European contingent claim about several securities is obtained. Finally, by using the Feynman-Kac theorem for Cauchy problem of extended Second-order parabolic equation obtained in [ 1 ] , the Black-Scholes pricing equation of European contingent claims of model is deduced.

关 键 词：跳跃扩散型随机微分方程 证券市场模型 股票价格 欧式未定权益 BLACK-SCHOLES方程 

分 类 号：F830.91[经济管理—金融学] O225[理学—运筹学与控制论]