基于不确定性测度相对熵的资产组合优化

Portfolio Optimization Based on the Measurement of Uncertainty with Relative Entropy

假设投资者是风险规避型,运用相对熵测度均值-方差模型参数不确定性程度,研究投资者在最坏情境下的资产组合优化问题。基于均值-方差模型,在相对熵某一正常数约束下构建描述资产组合优化问题的最小-最大化模型;运用拉格朗日法获得模型相应最优解,分析模型参数不确定性对资产组合优化的影响;最后,基于不同类型资产组合样本数据做对比性实证研究。结果表明:最坏情境下,随着模型参数不确定性程度增加,尽管投资者增加风险资产投资但资产组合业绩在下降;资产风险溢价不确定性对资产组合的影响强于风险溢价协方差不确定性;仅当相对熵低于风险中性测度相对熵时,投资者才会投资风险资产,否则离开金融市场;替代性投资有助于降低参数不确定性对资产组合优化的影响,提升资产组合业绩。研究不但为参数不确定性最坏情境下的资产组合优化问题提供了一个分析框架,而且为金融市场上的"非市场参与"现象提供了一个解释。

Assuming that investor is the characteristic of risk-aversion,this paper uses the relative entropy to measure the uncertainty degree of mean-variance model parameters,and studies the portfolio optimization problem in the worst scenario.Based on the mean-variance model,it constructs the min-max model to describe the portfolio optimization problem under the binding that relative entropy is a positive constant number;it applies the Lagrangian method to obtain the corresponding optimal solution of the model,and analyzes the influence of model parameters’ uncertainty on the portfolio optimization;at last,it comparatively does an empirical study based on sample data of different types of portfolio.Results show,in the worst scenario,portfolio performance is decreasing with the increasing of uncertainty degree of model parameters,although the investor increases its position on risky asset;the influence of risk premium uncertainty on portfolio is stronger than that of risk premium covariance uncertainty;the investor invests in risky assets only when the relative entropy is lower than that of the risk-neutral measurec otherwise,he leaves off the financial market;substitution investment helps to reduce the effect of parameters’ uncertainty on portfolio optimization,and improve the portfolio performance.The study not only provides an analytical framework for portfolio optimization in the worst scenario of parameters’ uncertainty,but also provides an explanation for the phenomenon of non-market participation in finance market.