学术
基于随机波动的企业的最优组合投资策略
周勇[1,2] 侯震梅[1,2] 刘三阳[2]
[1]新疆财经学院统计信息系,新疆乌鲁木齐830012 [2]西安电子科技大学应用数学系,陕西西安710071
摘 要:
Merton的投资模型拓展到随机波动模型．在典型的动态规划中，投资问题中的值函数一般用Bellman方程的粘滞解表示．本文通过指数变换把偏微分方程转变成一个半线性的抛物线方程，并证明了其值函数连续解的存在性，在此基础上给出了企业的最优组合投资策略及一个投资的例子．[著者文摘]
文章出处:
《应用数学》-2005年18卷4期 -547-552页
文献标识码:
A
文章编号:
1001-9847（2005）04-0547-06
The Optimal Investment Portfolio Policy Based on the Stochastic Volatility
ZHOU Yong , HOU Zhen-mei ,LIU San-yang （1. Xinjiang Institute of Finance and Economy, Urumchi 830012, China ;2.Department ofApplied Mathematics, Xidian University, Xi＇an 710071 ,China）
Abstract:
The investment model of the Merton is extended to the model with stochastic oscillation. In the dynamic programming of the classical, the value function is generally represented by the viscosity solution of the Stochastic partial differential equation in the investment problem. In this paper, the partial differential equation is transferred to a semi-llnear parabolic equation by using exponential transformation, meanwhile the existence of the continuous solution of the value function is proven. Furthermore,the optimal investment policy is obtained and an example is offered.[著者文摘]
Key words:
Stochastic oscillation; Partial differential equation; Exponential transformation ; Optimal investment portfolio
基金资助:
国家自然科学基金资助项目（69972036）
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