通胀和负债共同影响下时间一致的最优投资策略  

Time-Consistent Optimal Investment Strategy with Inflation and Liability Common Influence

作　　者：杨鹏[1] 刘琦[1] YANG Peng;LIU Qi(School of Science,Xijing University,Xi＇an 710123,China)

机构地区：[1]西京学院理学院,陕西西安710123

出　　处：《应用数学》2018年第4期723-730,共8页Mathematica Applicata

基　　金：陕西省自然科学基金资助(2016JM1032)

摘　　要：本文在通胀和负债影响下研究时间一致的投资策略选择问题.通胀和负债满足扩散过程,风险资产的价格用Levy过程刻画,并且考虑通胀、负债与风险资产之间的相关性.以最大化终止盈余的均值,同时最小化终止盈余的方差为目标,应用随机动态规划的方法研究该问题,得到最优时间一致投资策略和值函数的显式解.最后,通过数值计算,解释了通胀、负债对最优时间一致投资策略的影响.This paper studies an optimal time-consistent investment strategy selection problem with inflation and liability. The risky asset＇ price is governed by a Levy process while the inflation and liability evolves according to a Brownian motion with drift. The correlations between the risky asset and the inflation, and the liability are considered. Maximizing the expected terminal surplus while minimizing the variance of the terminal surplus is the objective. We investigate the problem by using the dynamic programming approach. Closed-form solutions for the optimal investment strategy and the corresponding value functions are obtained. Finally, through numerical calculation, we illustrate how the optimal investment strategy changes when inflation and liability parameters vary.

关 键 词：通胀 负债 时间一致 投资 随机控制 

分 类 号：O211.6[理学—概率论与数理统计]