Abstract Since security return cannot be accurately estimated using past data, in this paper it is assumed to take values in a given ellipsoidal uncertainty set. This paper aims to discuss a robust multi-objective portfolio selection problem based on the minimax regret criterion under an ellipsoidal uncertainty sets, in which the two objective functions are the portfolio return to be maximized and the mean absolute deviation as a risk measure to be minimized. The robust counterpart formulation for the proposed model is firstly presented, then an algorithm based on the relaxation procedure is designed to solve the robust counterpart formulation with second-order cone constraints and infinite constraints. Finally, a practical example based on real market data is presented to illustrate the effectiveness of the proposed model and the algorithm. Compared with the traditional robust portfolio model based on minimax robustness, the robust minimax regret optimal solutions proposed in this paper have better performance on several evaluation criteria.

中文翻译：

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具有椭球不确定性集的稳健多目标投资组合选择问题的极小极大后悔方法

摘要 由于使用过去的数据无法准确估计安全收益，因此本文假设取给定椭球不确定性集合中的值。本文旨在讨论在椭球不确定性集合下基于最小最大后悔准则的稳健多目标投资组合选择问题，其中两个目标函数是要最大化的投资组合收益和作为要最小化的风险度量的平均绝对偏差。 . 首先给出了所提出模型的鲁棒对应公式，然后设计了一种基于松弛过程的算法来求解具有二阶锥约束和无限约束的鲁棒对应公式。最后，给出了一个基于真实市场数据的实例来说明所提出的模型和算法的有效性。