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

  • Trutnau, Gerald
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911000706
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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 8 (August)
    Pages: 1845-1863

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:8:p:1845-1863
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    1. Marc Decamps & Marc Goovaerts & Wim Schoutens, 2006. "Self Exciting Threshold Interest Rates Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1093-1122.
    2. 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.
    3. Aleksandar Mijatović, 2010. "Local time and the pricing of time-dependent barrier options," Finance and Stochastics, Springer, vol. 14(1), pages 13-48, January.
    4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    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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