膨胀的Poisson过程及其在金融中的应用

本文定义了一种增量不独立的纯跳过程,称为膨胀的Poisson过程.采用了一个n跳过程来描述股票市场价格运动的规律,并构造了一个货币市场投资组合使得它的市场价值在指定时刻与股票价格相等,且该投资组合的收益被分解成为一个确定性的项和一个膨胀的Poisson项之和.证明了投资投票市场风险大于投资货币市场风险.

Dilated Poisson Processes and their Applications in Finance

A kind of pure jump processes with dependent increments,called dilated poisson processes,was defined.A generalized n-jump price process was used to describe the movement of stock price.Using this kind of stochastic processes,we decomposed the profit of the monetary market portfolio,generating the same cash flow at the pointed time as its stock market counterpart,into a deterministic term and a dilated Poisson term.It was showed that investment in stock market is more risky than in the monetary market,consisting with our observation of the real world.