不同借贷利率下的投资组合选择——-基于均值和VaR的效用最大化模型

用VaR代替方差来度量风险，从而把基于均值和方差的效用函数拓展为基于均值和VaR的一般二元效用函数（关于均值递增，关于VaR递减），进而研究含无风险资产且具有不同借贷利率时投资组合选择的效用最大化模型.利用均值-VaR模型有效边界的性质，得到了一般效用函数下最大效用存在的条件及最优解的本质特征，并给出了求解的具体方法和数值算法.最后作为结论的直接应用和说明，利用中国股票市场数据给出了一个实例分析.

Portfolio selection with different borrowing-lending rates:Utility maximization model based on mean and VaR

This paper uses VaR as a replacement of variance to measure risk and investigates a portfolio selection problem with different borrowing-lending rates. We consider a general utility function that is a function of only the mean and the VaR of portfolio return and establish a corresponding utility maximization model.Utilizing properties of the efficient frontier of the mean-VaR model, we obtain existence conditions and characterizations of the optimal solutions to the utility maximization model. Further we give a solution method and a numerical algorithm for the optional solution. Finally, as an application and a demonstration of our results, we give a numerical example using the real data of Chinese stock market.