Portfolio investment based on probabilistic multi-objective optimization and uniform design for experiments with mixtures

Introduction/purpose: In this paper, a new approach to solving the portfolio investment problem is formulated to handle simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return. Probability - based multi – objective optimization is combined with uniform design for experiments with mixtures to conduct processing. Methods: Preliminarily, probability - based multi – objective optimization is employed to synthesize the bi-objective problem of simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return into a single objective one of the total preferable probability of each alternative scenario. The total preferable probability is the product of all partial preferable probabilities of each performance utility; subsequently, the method of uniform design for experiments with mixtures is used to create a set of effective sampling points for the portfolio investment problem to provide discretization in data processing and simplifying treatment, of which the proportion xi follows the constraint condition of xl + x2 + x3．．．+ xs = 1 with the total number of variables s for xi. Results: The new approach is used to deal with the portfolio Investment problem that is, in essence, simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return, which leads to reasonable consequences. The results are with the quality of rationality from the respect of the probability theory for simultaneous optimization of multiple objectives. Conclusion: This method naturally reflects the essence of the portfolio investment problem and opens a new way of solving the relevant problem.