Work

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

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.07765

Author: Yang, Shuzhen

Institution: Shandong University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Shandong University, National Natural Science Foundation of China

Award: G3609560599

OpenAlex ID: W4415318434

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