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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mingli Zhang & Gaofeng Zong, 2023. "From Transience to Recurrence for Cox–Ingersoll–Ross Model When b < 0," Mathematics, MDPI, vol. 11(21), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4485-:d:1270656
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    References listed on IDEAS

    as
    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
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