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Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve

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  • Trutnau, Gerald

Abstract

Let [sigma],[delta]>0,b>=0. Let , be continuous, and locally of bounded variation. We develop a general analytic criterion for the pathwise uniqueness of where p[set membership, variant](0,1), and is the symmetric semimartingale local time of R-[lambda]2. The criterion is related to the existence of nice (Kummer) functions for the time dependent infinitesimal generator of R. As a corollary we obtain explicit sufficient conditions for pathwise uniqueness. These are expressed in terms of [lambda]2, its derivative, and the parameters [sigma],[delta],b,p.

Suggested Citation

  • Trutnau, Gerald, 2011. "Pathwise uniqueness of the squared Bessel and CIR processes with skew reflection on a deterministic time dependent curve," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1845-1863, August.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:8:p:1845-1863
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    1. Ouknine, Y., 1993. "Quelques identités sur les temps locaux et unicité des solutions d'équations differentielles stochastiques avec reflection," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 335-340, November.
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    5. Trutnau, Gerald, 2010. "Weak existence of the squared Bessel and CIR processes with skew reflection on a deterministic time-dependent curve," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 381-402, April.
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    Cited by:

    1. Shiyu Song & Guangli Xu & Yongjin Wang, 2016. "On First Hitting Times for Skew CIR Processes," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 169-180, March.
    2. Guangli Xu & Shiyu Song & Yongjin Wang, 2016. "The Valuation Of Options On Foreign Exchange Rate In A Target Zone," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-19, May.
    3. Étoré, Pierre & Martinez, Miguel, 2018. "Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2642-2687.
    4. Tian, Yingxu & Zhang, Haoyan, 2018. "Skew CIR process, conditional characteristic function, moments and bond pricing," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 230-238.
    5. Xu, Guangli & Wang, Yongjin, 2016. "On stability of the Markov-modulated skew CIR process," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 139-144.
    6. Guangli Xu & Xingchun Wang, 2021. "On the Transition Density and First Hitting Time Distributions of the Doubly Skewed CIR Process," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 735-752, September.

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