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The Maximum Principle with Terminal State Constraints for Optimal Control of Mean-Field FBSDE Driving by Teugels Martingales
  • Zhen Huang,
  • Ying Wang,
  • Xiangyun Lin
Zhen Huang
Shandong University of Science and Technology
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Ying Wang
Shandong University of Science and Technology

Corresponding Author:[email protected]

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Xiangyun Lin
Shandong University of Science and Technology
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Abstract

This paper studies the problem of optimal control with state constraints for mean-field type stochastic systems, which is governed by fully coupled forward-backward stochastic differential equations(FBSDE) with Teugels martingales. In this system, the coefficients contain not only the state processes but also its marginal distribution, and the cost function is of mean-field type as well. We use an equivalent backward formulation to deal with the terminal state constraint, and then we obtain a stochastic maximum principle by Ekeland’s variational principle. In addition, we discuss a stochastic LQ control problem with state constraints.
23 Mar 2023Submitted to Optimal Control, Applications and Methods
27 Mar 2023Submission Checks Completed
27 Mar 2023Assigned to Editor
27 Mar 2023Review(s) Completed, Editorial Evaluation Pending
29 Jul 2023Reviewer(s) Assigned
12 Feb 2024Editorial Decision: Accept