基于学习行为的动态资产组合选择

The Choice of Dynamic Portfolio based on the Learning Behavior

在不完全信息下,研究了风险资产收益前两阶矩的参数不确定性对动态资产组合选择的影响.在连续时间下假设资产的价格服从随机扩散过程,引入参数不确定性,利用随机动态规划方法推导出风险资产最优配置的封闭解,使投资者的终期财富期望幂效用最大;在离散时间下假设风险资产的连续复合月收益率服从独立同分布的正态分布,通过贝叶斯学习准则,以上证综合指数不同区间段的两个样本做实证研究.研究表明,当投资者的风险规避程度大于(小于)对数效用时,参数不确定性将导致负(正)的投资期效应;当投资者在估计过程中运用较多的历史数据、或者风险规避程度增加时,参数不确定性的影响将减弱;收益一阶矩的不确定性影响较其二阶矩强.研究突出了参数不确定性在动态资产组合选择过程中的重要性.

This paper studies the effects of parametric uncertainty of the first two moments about risky asset return on the choice of dynamic portfolio under incomplete information. In continuous-time framework, assuming that asset price follows stochastic diffusion process, it introduces parametric uncertainty, and applies stochastic dynamic programming to derive the closed-form solution of optimal portoho choice, which maximizes the expected power utility of investor＇s terminal wealth; in discrete-time framework, continuous compounding monthly returns of risky asset are assumed to be normal i.i.d., it applies the rule of Bayesian learning to do empirical study about two different sample of Shanghai Exchange Composite Index. Result shows, the uncertainty of parameter leads to negative （positive） investment horizon effects when investor＇s risk aversion is more （less） than that of logarithmic utility; the effects of parametric uncertainty will weaken when investor uses more past data in his estimation, or when his risk aversion increases; the effect of the first order moment＇s uncertainty is stronger than that of the second order moment＇s uncertainty. This study stresses the importance of parametric uncertainty in the context of dynamic portfolio choice.