基于CVaR投资组合优化问题的光滑化方法

对选定的风险资产进行组合投资,以条件风险价值(CVaR)作为度量风险的工具,建立单期投资组合优化问题的CVaR模型。目标函数中含有多重积分与plus函数,产生情景矩阵将多重积分计算转化成求和运算,提出plus函数的一个新的一致光滑逼近函数并给出求解CVaR模型的光滑化方法,最后的实证研究表明了本文算法的优越性。

A Smoothing Method for Portfolio Optimization Based on CVaR

Portfolio investment on the given risky assets is considered in this paper. At first, we develop a CVaR model for the single phase portfolio optimization problem, using CVaR as the risk measure. Noticing that both multi-integral and plus function are contained in the objective function, we convert multi-integral calculation into summation operator by producing a scenario matrix. Then, we propose a new consistent smooth approximating function of the plus function and give a smoothing method for solving CVaR model at the same time. Finally, we give two empirical studies which illustrate the superiority of our algorithm.