First‐Hitting Optimal Control Model for Portfolio Problem and Intelligent Optimization Algorithms Resolutions

ABSTRACT To address the issues of existing optimal control models for investment portfolios neglecting multivariable coupling effects, time constraints, and uncertainty, this study proposes a multivariable optimal control model with a first‐hitting property by integrating the influences of multivariable control with the time factor of optimal control. Based on the ‐path definition, the uncertain model is transformed into a deterministic one; this deterministic model is then applied to the multi‐period investment portfolio scenario, leading to the development of two types of multi‐asset models: The optimistic‐value model and the predefined values model. By leveraging the first‐hitting time theory, the sufficient conditions for the existence of optimal control vectors in these two sub‐models are derived. Considering the global convergence and robustness of the differential evolution algorithm in solving multivariable and multi‐constraint problems, this study combines the sufficient conditions for the existence of the model's optimal control vectors with this algorithm and analyzes the impact of changes in relevant model parameters on the optimal control effect. Finally, monthly closing price data (from 2021 to 2025) of four representative stocks and one government bond are selected as empirical samples to verify the accuracy and practicality of the proposed model. The innovations of this study are as follows: (1) Integrating the time factor with multivariable control to propose a multivariable control model with the first‐hitting property; (2) Combining the existence conditions of optimal control vectors with intelligent algorithms to enhance the reliability of solution‐finding.