摘要
在最优消费与证券选择问题中,假定投资市场有两种资产可供选择:一种为无风险资产(银行债券),另一种为风险资产(股票).由于受重大信息的影响,风险资产的价格往往会产生跳跃.文章研究了这种带跳跃的投资问题,用泊松过程与布朗运动模拟了投资者的财富过程.为使投资者在整个生命周期的消费效用期望值最大,在跳跃幅度为一随机变量的条件下,利用贝尔曼动态规划原理,导出了最优消费及投资策略所满足的方程组,并且在跳跃幅度的概率分布已知的情况下,针对具体的参数值,给出了最优初始策略的数值解与最大消费效用期望值.
This paper examines an optimal strategy problem on consumption and portfolio. In this problem, we assume there are two assets to invest in for investors. One is risk-free asset（e, g., bond）, the other is risky asset （e. g., stock）. Investor can choose the investing proportion of assets to maximize his expected lifetime utility. In most situations, the price of risky assets will jump when some important information come, so it is significant to study this problem. This paper discusses this case in which the jump range is a stochastic variable, and gives the evolving process of his wealth that is modeled by Poisson process and Brownian motion. By using Bellman dynamic programming principle, we induce the equations that the optimal strategies satisfy. If the probability distribution of jump range is known, we can obtain its＇explicit numerical solution to the equations for some concrete values of parameters. Moreover, we can get the value of the expected lifetime utility.
出处
《管理科学学报》
CSSCI
北大核心
2005年第6期83-87,共5页
Journal of Management Sciences in China
基金
国家自然科学基金资助项目(19671004)
关键词
随机跳跃幅度
贝尔曼动态规划原理
泊松过程
布朗运动
最优消费与证券选择策略
stochastic jump-range
Bellman dynamic programming principle
Poisson process
Brownian motion
optimal consumption and portfolio strategies
