2024/11/10 by Siyu Lv, Zhen Wu, Lv, Siyu +5
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2411.06522
openalex publication_date 2024/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical framework for such kind of problem. First, based on the dynamic programming principle, the value function of the optimal stopping problem is characterized as the unique viscosity solution to the associated Hamilton-Jacobi-Bellman equation. Then, the so-called smooth-fit principle for optimal stopping problems is proved in the current context, and a verification theorem consisting of a set of sufficient conditions for robust optimality is established. Moreover, when the Markov chain has a large state space and exhibits a two-time-scale structure, a singular perturbation approach is utilized to reduce the complexity involved and obtain an asymptotically optimal solution. Finally, an example of choosing the best time to sell a stock is provided, in which numerical experiments are reported to illustrate the implications of model uncertainty and regime switching.