Optimal investment problem with delay under partial information
Optimal investment problem with delay under partial information
复制标题
部分信息下的时滞最优投资问题
DOI：
10.3934/mcrf.2020001
复制
发表时间：
2019
影响因子：
1.2
通讯作者：
Xin Zhang
中科院分区：
文献类型：
--
作者：
Shuaiqi Zhang;Jie Xiong;Xin Zhang
本文研究了部分信息下具有时滞的最优投资问题。我们假设金融市场由一种无风险资产（债券）和一种风险资产（股票）组成，从金融市场只能观察到风险资产的价格。投资者的目标是最大化终端财富的预期效用和路径段的平均值。利用滤波理论，建立了分离原理，将问题归结为完全信息情形。通过求解相应的Hamilton-Jacobi-Bellman方程，得到了价值函数和最优策略的显式表达式。此外，我们还研究了最优投资策略对模型参数的敏感性，并对完全信息方案和部分信息方案进行了数值模拟和比较。
In this paper, we investigate the optimal investment problem in the presence of delay under partial information. We assume that the financial market consists of one risk free asset (bond) and one risky asset (stock) and only the price of the risky asset can be observed from the financial market. The objective of the investor is to maximize the expected utility of the terminal wealth and average of the path segment. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. Explicit expressions for the value function and the corresponding optimal strategy are obtained by solving the corresponding Hamilton-Jacobi-Bellman equation. Furthermore, we study the sensitivity of the optimal investment strategy on the model parameters in a numerical section and both of the full and partial information schemes are simulated and compared.