基于BE-散度的不确定投资组合优化问题的等价形式

Equivalent form of uncertain portfolio optimization problem on BE-divergence

对于投资组合的优化问题,当目标函数和约束条件中具有不确定性时,应用Burg entropy-散度(BE-散度)理论、测度转化、对偶理论等将这类问题等价为在经验分布p_0下不具有鲁棒性的投资组合优化问题.具体地,将优化模型中的约束函数,利用经验数据得到经验分布,考虑经验分布与未知分布的Burg entropy-散度的距离,构造分布p的不确定集,对于定义在不确定集上的目标函数和约束函数,利用测度转换,将参数对于未知分布的极小化问题转化为似然比对于经验分布的凸优化问题,应用对偶理论得到等价的约束函数,从而得到分布鲁棒投资组合优化问题的等价形式.

For portfolio optimization problems with uncertainties in objective functions and constraints,Burg entropy-divergence theory,the measure transformation and duality theory are applied to treat these problems as portfolio optimization problems without robustness under empirical distribution.Specifically,considering the constraint function in the optimization model,the empirical distribution is obtained from the empirical data,and the distance between the empirical distribution and the Burg entropy-divergence of the unknown distribution is considered.For the objective function and the constraint function defined on the uncertainty set,the parameter is transformed to the unknown distribution by the measure.The minimization problem is transformed into a convex optimization problem with likelihood ratio for empirical distribution.The equivalent constraint function is obtained by applying the dual theory,and the equivalent form of the distributed robust portfolio optimization problem is obtained.