跳跃股价模型下投资组合的生成函数  

Portfolio generating functions with stock price jumps

作　　者：初云浩[1] 叶俊[1] 

机构地区：[1]清华大学数学科学系,北京100084

出　　处：《清华大学学报（自然科学版）》2003年第12期1699-1702,共4页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(79970120;10001021)

摘　　要：针对股价的非连续模型,为研究投资组合之间收益的关系,采用半鞅的分析办法,研究由Ito过程和Poisson过程复合的股价模型下的投资组合生成函数及其性质。随机组合理论表明通过构造生成函数可以生成新的投资组合,并证明了生成组合的权重表达式以及相应的漂移过程项和跳跃过程项。因而可以通过一个随机微分方程分析生成投资组合的收益和市场资产组合的收益,以及收益的期望控制的关系。结论表明生成函数及相关函数在满足一定条件下这样的期望控制关系存在。The portfolio generating function was used to analyze portfolios profits using the semi-Martingale method in a stock market with a jumping stock price driven by an Ito process and a Poisson point process. The theory of stochastic portfolios shows that the function can generate a dynamic equity portfolio. The expressions for the weights of the generated portfolio, the corresponding drift process and the jump process relate the generated portfolio and the market portfolio. Hence, this method can be used to analyze profits and relative values of the two portfolios through a stochastic differential equation. A certain condition can be given to establish an expected dominance relationship between the two portfolios.

关 键 词：跳跃股价模型 生成函数 概率论 金融市场 市场投资组合 生成投资组合 期望控制 

分 类 号：F830.59[经济管理—金融学] F224.7