Multi-objective Distribution Robust Optimization Based On Set Order And DBSCAN Algorithm Quantifies Investment Strategy

Many decision problems in science,engineering and economics are affected by uncertain parameters.This paper mainly considers how to enhance the robustness of multi-objective portfolio optimization solutions.Since the uncertainty of input parameters exists objectively,it is the core of multi-objective robust optimization to construct a pessimistic model based on the uncertainty set of parameters.Different from the common form of uncertainty set in the existing literature,the uncertainty set in this paper is constructed based on the probability density space under Wasserstein’s metric.Using Wasserstein measures,we construct a sphere in a space of(multivariate and non-discrete)probability distributions centered on a uniform distribution over the training sample,and look for the best-performing decision under the worst-case distribution within this Wasserstein sphere.Firstly,in order to solve the uncertain portfolio optimization problem in various extreme cases,a multiobjective optimization model is established,and the concepts of three effective solutions are given by means of several kinds of set order relations.Then,according to the ideas of Ben-Tal and Nemirofs,several multi-objective robust corresponding methods are introduced,and the pessimistic model is solved by an improved multiobjective particle swarm optimization method.Finally,the closed-loop logic of portfolio is realized by combining density spatial clustering algorithm.