Uncertain random portfolio optimization with non-dominated sorting genetic algorithm-II and optimal solution criterion

The complexity of the financial systems inevitably leads to the uncertain information and random information simultaneously. Because asset returns frequently show excessive kurtosis and tend to be skewed, we consider an uncertain random higher moments portfolio optimization problem in this paper, in which uncertain and random return rates exist simultaneously. First, the concept of kurtosis for uncertain random variable is defined and the deterministic expressions of kurtosis under three kinds of distributions are derived. Then, an uncertain random mean-variance-skewness-kurtosis-entropy model is formulated with two auxiliary models for portfolio optimization problem. After solving the equivalent deterministic model with NSGA-II algorithm, we propose a new optimal solution criterion for finding a single optimal solution in Pareto optimal solution set. Finally, we present a numerical simulation and obtain the following results: (i) the practicability and the validity of the proposed model, the NSGA-II algorithm and the optimal selection criterion have verified; (ii) the size of population has an obvious influence on the single optimal solution; (iii) the parameter adjustment has a significant impact on the results, and the results are in perfect agreement with the actual situation.

Automated summary

This paper addresses the uncertainty and randomness in financial systems, specifically focusing on the problem of uncertain random higher moments portfolio optimization. Through the proposal of a new uncertain random mean-variance-skewness-kurtosis-entropy model, along with two auxiliary models, the authors provide a comprehensive framework for portfolio optimization. Numerical simulation results confirm the practicality and validity of the proposed model, the NSGA-II algorithm, and the optimal selection criterion, with population size and parameter adjustment found to significantly impact the results, aligning with real-world observations.