Academic Report of School of Mathematical Sciences [2026] No. 003

(Series Report for High-Level University Construction No. 1262)

Title：Finite-Horizon Optimal Consumption and Investment Problem with Endogenously Updating Consumption Bounds

Speaker：Professor Zhou Yang  (South China Normal University)

Time：10:30-11:30, Jan. 9, 2026

Location：Room 303, Alumni Plaza

Abstract：This paper addresses the finite-horizon utility maximization problem faced by an agent who dynamically updates their consumption bounds, determined by a minimum consumption level process. The agent derives utility from both the consumption process and the minimum consumption level, incurring a proportional utility cost with each adjustment. Using the dual-martingale approach, we formulate the dual problem as a finite-horizon two-sided singular control problem. By exploring the relationship between singular control and switching control, we transform the dual problem into a set of optimal switching problems, which we then simplify to a single parabolic double obstacle problem. Employing advanced and non-trivial PDE techniques, we thoroughly delineate the analytical properties of the double obstacle problem and its two free boundaries. From this analysis, we construct the optimal singular control for the dual problem using a carefully selected set of switching controls. We conclude by establishing a duality theorem and deriving the optimal strategies in feedback form.

Speaker Profile：Zhou Yang , Professor and Doctoral Supervisor, School of Mathematical Sciences, South China Normal University. His research focuses on financial mathematics and stochastic control, with primary areas including American derivative pricing, optimal portfolio selection, optimal stopping problems, and free boundary problems in finance. Selected research findings have been published in journals such as FINANCE & STOCHASTIC PROCESSES, MATHEMATICAL OPERATIONS RESEARCH, SIAM JOURNAL OF CONTROL AND OPTIMIZATION, SIAM JOURNAL OF FINANCIAL MATHEMATICS, SIAM J MATH ANAL, and J DIFFER EQUATIONS. He has led six National Natural Science Foundation projects and multiple provincial/ministerial-level research grants.                

Faculty and students are welcome to attend!

Invited by: Jingchao Li

School of Mathematical Sciences

January 5, 2026