From Transience to Recurrence for Cox–Ingersoll–Ross Model When b < 0

Mingli Zhang and Gaofeng Zong ()
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Mingli Zhang: School of Science, Shandong Jianzhu University, Jinan 250101, China
Gaofeng Zong: School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China

Mathematics, 2023, vol. 11, issue 21, 1-23

Abstract: We consider the Cox–Ingersoll–Ross (CIR) model in time-dependent domains, that is, the CIR process in time-dependent domains reflected at the time-dependent boundary. This is a very meaningful question, as the CIR model is commonly used to describe interest rate models, and interest rates are often artificially set within a time-dependent domain by policy makers. We consider the most fundamental question of recurrence versus transience for normally reflected CIR process with time-dependent domains, and we examine some precise conditions for recurrence versus transience in terms of the growth rates of the boundary. The drift terms and the diffusion terms of the CIR processes in time-dependent domains are carefully provided. In the transience case, we also investigate the last passage time, while in the case of recurrence, we also consider the positive recurrence of the CIR processes in time-dependent domains.

Keywords: transience; recurrence; CIR model; time-dependent region; reflection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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