| Author: | Li, Yunhong |
| Title: | Optimal control and stopping : stochastic linear quadratic control problems in non-markovian regime switching system |
| Advisors: | Xu, Zuoquan (AMA) |
| Degree: | Ph.D. |
| Year: | 2026 |
| Department: | Department of Applied Mathematics |
| Pages: | xiv, 127 pages : illustrations |
| Language: | English |
| Abstract: | This thesis investigates a mixed stochastic linear quadratic control-stopping problem with non-Markovian regime switching and random coefficients, where the control pair consists of a classical control variable and a controlled stopping time. Both homogeneous and non-homogeneous cases are considered. For homogeneous problem, the primary contributions include the explicit derivation of optimal state feedback controls and optimal cost values via several novel systems of extended stochastic Riccati equations (ESREs) and reflected extended stochastic Riccati equations (RESREs). For non-homogeneous problem, we give a lower boundary. These ESREs and RESREs are either highly nonlinear or involve unbounded coefficients, presenting significant analytical challenges. A major achievement of this work is the establishment, for the first time, of a multidimensional comparison theorem for reflected backward stochastic differential equations (RBSDEs). Building on this result, and employing advanced techniques such as truncation functions, logarithmic transformations, the John-Nirenberg inequality, and BMO (Bounded Mean Oscillation) martingale estimates, we prove the existence and uniqueness of solutions to the aforementioned ESREs and RESREs. In addressing the solvability of linear reflected BSDEs with unbounded coefficients, we first resolve the one-dimensional case and then extend the result to the multidimensional setting using the contraction mapping method. |
| Rights: | All rights reserved |
| Access: | open access |
Copyright Undertaking
As a bona fide Library user, I declare that:
- I will abide by the rules and legal ordinances governing copyright regarding the use of the Database.
- I will use the Database for the purpose of my research or private study only and not for circulation or further reproduction or any other purpose.
- I agree to indemnify and hold the University harmless from and against any loss, damage, cost, liability or expenses arising from copyright infringement or unauthorized usage.
By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms.
Please use this identifier to cite or link to this item:
https://theses.lib.polyu.edu.hk/handle/200/14650