负债情形下效用投资组合选择的最优控制  

Optimal Control for Utility Portfolio Selection with Liability

作　　者：常浩[1,2] 荣喜民[3] 

机构地区：[1]天津工业大学数学系,天津300387 [2]天津大学管理学院,天津300072 [3]天津大学理学院,天津300072

出　　处：《应用概率统计》2012年第5期457-470,共14页Chinese Journal of Applied Probability and Statistics

基　　金：教育部人文社会科学研究青年基金(11YJC790006);天津市高等学校科技发展基金(20100821);天津市自然科学基金(09JCYBJC01800)资助

摘　　要：应用随机最优控制理论研究负债情形下基于效用最大化的动态投资组合.假设负债是服从几何布朗运动的随机过程且与股票价格完全相关,应用动态规划原理得到值函数满足的HJB方程,并对幂效用、指数效用和对数效用函数下的最优投资策略进行系统研究.文章首先通过变量替换方法求解相应的HJB方程得到幂效用和指数效用函数下最优投资策略的显示表达式,然后通过Legendre变换-对偶方法得到对数效用函数下最优投资策略的显示表达式.最后给出算例解释本文所得结论,并分析市场参数对最优投资组合的影响.In this paper we use stochastic optimal control theory to investigate a dynamic portfolio selection problem with liability process, in which the liability process is assumed to be a geometric Brownian motion and completely correlated with stock prices. Hamilton-Jacobi-Bellman （HJB） equations for the We apply dynamic programming principle to obtain value function and systematically study the optimal investment strategies for power utility, exponential utility and logarithm utility. Firstly, the explicit ex- pressions of the optimal portfolios for power utility and exponential utility are obtained by applying variable change technique to solve corresponding HJB equations. Secondly, we apply Legendre transform and dual approach to derive the optimal portfolio for logarithm utility. Finally, numerical examples are given to illustrate the results obtained and analyze the effects of the market parameters on the optimal portfolios.

关 键 词：负债过程 动态投资组合 动态规划原理 LEGENDRE变换 幂效用 指数效用 对数效用. 

分 类 号：F830.48[经济管理—金融学] O211.6[理学—概率论与数理统计]