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Some results on strong solutions of SDEs with applications to interest rate models

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  • Wissel, Johannes

Abstract

In this work, we investigate SDEs whose coefficients may depend on the entire past of the solution process. We introduce different Lipschitz-type conditions on the coefficients. It turns out that for existence and uniqueness of a strong solution it suffices to have Lipschitz continuity in mean, in a sense to be made precise. We then investigate when it suffices to have local Lipschitz conditions. Furthermore we consider the case of drift coefficients which are locally Lipschitz in mean. Finally we show how these results can be applied to prove existence and uniqueness of solutions in interest rate term structure models.

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  • Wissel, Johannes, 2007. "Some results on strong solutions of SDEs with applications to interest rate models," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 720-741, June.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:6:p:720-741
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    References listed on IDEAS

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    1. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. M. Krivko & M. V. Tretyakov, 2011. "Numerical integration of Heath-Jarrow-Morton model of interest rates," Papers 1109.2557, arXiv.org.
    2. Dan Pirjol & Lingjiong Zhu, 2019. "Explosion in the quasi-Gaussian HJM model," Papers 1908.07102, arXiv.org.
    3. Martin Schweizer & Johannes Wissel, 2008. "Arbitrage-free market models for option prices: the multi-strike case," Finance and Stochastics, Springer, vol. 12(4), pages 469-505, October.
    4. Dan Pirjol & Lingjiong Zhu, 2018. "Explosion in the quasi-Gaussian HJM model," Finance and Stochastics, Springer, vol. 22(3), pages 643-666, July.

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