Work

Large deviations for Cox–ingersoll–ross processes with state-dependent fast switching

Year: 2026

Type: article

Abstract: We study large deviations for Cox–Ingersoll–Ross processes with small noise and state-dependent fast switching via associated Hamilton–Jacobi–Bellman equations. As time scales separate, when the noise goes to 0 and the rate of switching goes to normal infinity ∞ $\infty$ , we get a limit equation characterized by the averaging principle. Moreover, we prove the large deviation principle with an action-integral form rate function to describe the asymptotic behavior of such systems. The new ingredient is establishing the comparison principle in the singular context. The proof is carried out using the nonlinear semigroup method from Feng and Kurtz’s book [14].

Source: Journal of Applied Probability

DOI: 10.1017/jpr.2026.10081

Authors: Yanyan Hu, Richard C. Kraaij, Fubao Xi

Institutions: University of Science and Technology Beijing, Delft University of Technology, Beijing Institute of Technology

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, China Scholarship Council

Awards: G1496148395, 机制切换随机系统及其应用