基于随机基准的最优投资组合选择问题研究  

Optimal Portfolio Selection Problem Based on Stochastic Benchmark

作　　者：林祥[1] 斯梦霞 钱艺平 LIN Xiang;SI Mengxia;QIAN Yiping(School of Finance,Zhejiang Gongshang University,Hangzhou 310018,China)

机构地区：[1]浙江工商大学金融学院,浙江杭州310018

出　　处：《应用数学》2020年第2期449-462,共14页Mathematica Applicata

基　　金：浙江省自然科学基金(LY17A010005);教育部人文社科基金(18YJA790051、19YJE790001)。

摘　　要：本文研究基于随机基准的最优投资组合选择问题.假设投资者可以投资于一种无风险资产和一种风险股票,并且选择某一基准作为目标.基准是随机的,并且与风险股票相关.投资者选择最优的投资组合策略使得终端期望绝对财富和基于基准的相对财富效用最大.首先,利用动态规划原理建立相应的HJB方程,并在幂效用函数下,得到最优投资组合策略和值函数的显示表达式.然后,分析相对业绩对投资者最优投资组合策略和值函数的影响.最后,通过数值计算给出了最优投资组合策略和效用损益与模型主要参数之间的关系.In this paper we investigate the portfolio selection problem based on a stochastic benchmark.Investor can invest her wealth in a financial market consisting of a risk-free asset and a risky stock.The benchmark is driven by a stochastic process and is correlated with the risky stock.Investor chooses a dynamic portfolio strategy in order to maximize her expected terminal absolute wealth and relative wealth utility.By invoking the use of the dynamic programming principle,the corresponding HJB equation is established.Furthermore,closed-form expressions of the optimal portfolio strategy and the value function under the investor with a power utility function are derived.The effects of the relative performance on the optimal portfolio strategy and the value function are also analyzed.Finally,numerical examples are provided to illustrate how the optimal portfolio strategy and the utility profit change when some model parameters vary.

关 键 词：随机基准 投资组合 相对业绩 效用损益 

分 类 号：O211.67[理学—概率论与数理统计]