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


  • Trutnau, Gerald


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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    References listed on IDEAS

    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.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Aleksandar Mijatović, 2010. "Local time and the pricing of time-dependent barrier options," Finance and Stochastics, Springer, vol. 14(1), pages 13-48, January.
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    Cited by:

    1. repec:eee:apmaco:v:329:y:2018:i:c:p:230-238 is not listed on IDEAS
    2. Xu, Guangli & Wang, Yongjin, 2016. "On stability of the Markov-modulated skew CIR process," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 139-144.


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