Uncertain utility portfolio optimization based on two different criteria and improved whale optimization algorithm - Xu, Jiajun; Li, Bo (Expert systems with applications, 2025)
Since Markowitz introduced the mean–variance model, many investors have described investment return rates by assuming they are stochastic or fuzzy variables. However, the inherent complexity and unpredictability of financial markets often render these assumptions insufficient. To address these challenges, an increasing number of researchers are exploring portfolio optimization within the framework of uncertainty theory. This paper proposes two portfolio optimization models that incorporate investors’ utility under the criteria of expected value and optimistic value. We derive the deterministic forms of these two models under the assumption that the variables follow uncertain normal distributions. Additionally, we compare the differences between the multi-factor expected value-standard deviation utility (ESU) model and the optimistic value-standard deviation utility (OSU) model in terms of their ability to maximize investors’ utility. To solve these models effectively, we propose an improved whale optimization algorithm (IWOA) based on the Levy flight strategy, adaptive position weight strategy, and adaptive probability threshold. Extensive numerical experiments validate the effectiveness of the improved algorithm and compare the differences between the two models.