组合投资选择的随机最优控制方法  

Stochastic Optimal Control Method for Portfolio Selection

作　　者：荣幸[1] 

机构地区：[1]天津大学理学院数学系,天津300072

出　　处：《工程数学学报》2014年第2期159-165,共7页Chinese Journal of Engineering Mathematics

基　　金：天津市自然科学基金(09JCYBLJC01800)~~

摘　　要：基于随机利率和负债的组合投资选择研究,无论在理论上还是实际应用中都有着重要的意义.本文假设利率服从Vasicek过程,在终端财富期望效用最大化目标下,建立考虑负债和固定比例交易成本的最优组合投资模型.应用最大值原理得到相应问题值函数的HJB方程,通过Legendre变换-对偶方法将难以直接求解的非线性的HJB方程转化为线性的二阶偏微分方程,并对对数效用函数,得到了对数效用函数下最优投资策略的解析表达式.It is of great importance to study portfolio selection with stochastic interest rates and liability for both theoretical analysis and practical applications. In this paper, on maxi-mizing the expected utility of terminal wealth, the interest rate is supposed to be satisfied with the Vasicek process, and the optimal investment problem with liability and fixed proportion transaction cost is established. HJB equation of the value function of the optimal investment problem with liability is obtained by the maximum principle, and nonlinear HJB equation is tranformed into linear PDE by Legendre transform-dual method. Furthermore, the closed-form solutions of the optimal investment strategy is derivied under the logarithmic utility function.

关 键 词：VASICEK模型 负债管理 HJB方程 Legendre变换-对偶方法 对数效用 

分 类 号：F830.48[经济管理—金融学]