Portfolio bi-objective optimization with uncertain Hurwicz criterion and uncertain programming

The occurrence of unforeseeable events, such as public health emergencies, financial crises, and military conflicts, significantly increases the level of uncertainty in financial markets. In addition, it is common to encounter challenges such as insufficient sample data and vague expressions in real financial markets. In this paper, we delve into the study of an uncertain portfolio optimization problem by incorporating uncertainty theory and Hurwicz criterion with insufficient sample data and vague expressions. First, we introduce the uncertain Hurwicz criterion and analyze its mathematical properties. Then an uncertain bi-objective portfolio optimization model under Hurwicz criterion with considering investment diversification is formulated. And, a three steps method is applied to turn it into two models that are dedicated to optimizing a single objective. Furthermore, we estimate the unknown parameters of uncertain return rates when there are a small number of observed data. Finally, we conduct numerical simulations to verify the suitability of the uncertain Hurwicz criterion and the models proposed.