Academic Report of School of Mathematical Sciences [2026] No. 080

(Series Report for High-Level University Construction No. 1339)

Title：Comparison theorems for multi-dimensional BSDEs with jumps and applications to constrained stochastic linear-quadratic control

Speaker：Xiaomin Shi, Associate Professor (Shandong University of Finance and Economics)

Time：16:00-17:00, July 22, 2026

Location：Room 514, Huixing Building, Yuehai Campus, Shenzhen University

Abstract: In this talk, I will present two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for one-dimensional case. Using these and other delicate tools, we then construct solutions to coupled two-dimensional stochastic Riccati equation with jumps in both standard and singular cases. In the end, these results are applied to solve a cone-constrained stochastic linear-quadratic control problem and a mean-variance portfolio selection problem with jumps. Different from no jump problems, the optimal (relative) state processes may change their signs, which is of course due to the presence of jumps. This talk is based on a joint work with Prof. Ying Hu and Prof. Zuo Quan Xu.

Speaker Profile：Xiaomin Shi earned her Ph.D. in Financial Mathematics and Financial Engineering from Shandong University and is currently an associate professor in the School of Statistics and Mathematics at Shandong University of Finance and Economics. Her research interests include directional stochastic differential equations, stochastic control, and financial mathematics. Her work has been published in academic journals such as Annals of Applied Probability, SIAM Journal on Control and Optimization, SIAM Journal on Financial Mathematics, ESAIM: Control, Optimisation and Calculus of Variations, and Applied Mathematics and Optimization.

Faculty and students are welcome to attend!

Invited by: Hanxiao Wang

School of Mathematical Sciences

July 21, 2026