Minimum-Time Stochastic Optimal Control Problems Under Mean Constraints and Application to Portfolio Investment

Abstract

Motivated by the practical demand for minimum-time optimal investment problems, we develop a unified framework for mean constraints minimum-time stochastic optimal control problems. In this setting, the minimum-time criterion is defined as the expected earliest time to reach a target state, making the terminal time dependent on the control. The main contributions of this work are twofold: first, we derive an extended stochastic maximum principle for the proposed model and further prove the existence of an optimal control for the linear systems; second, we establish a bang-bang type optimal control for the linear time-optimal control problem. In the end, we solve a financial portfolio optimization problem within the proposed framework.