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Long time behaviour of stochastic interest rate models

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  • Zhao, Juan

Abstract

In this paper, we study the long time behaviour of two classes of stochastic interest rate models. Suppose that x(t) is a one-factor interest rate model with positive jumps. For a suitable constant we prove that converges almost surely as t-->[infinity]. A similar result is also proved for a two-factor affine model.

Suggested Citation

  • Zhao, Juan, 2009. "Long time behaviour of stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 459-463, June.
  • Handle: RePEc:eee:insuma:v:44:y:2009:i:3:p:459-463
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    3. Griselda Deelstra & Freddy Delbaen, 1998. "Long-term returns in stochastic interest rate models: different convergence results," ULB Institutional Repository 2013/7582, ULB -- Universite Libre de Bruxelles.
    4. 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..
    5. Griselda Deelstra & Freddy Delbaen, 1995. "Long-term returns in stochastic interest rate models," ULB Institutional Repository 2013/7578, ULB -- Universite Libre de Bruxelles.
    6. Deelstra, G. & Delbaen, F., 1995. "Long-term returns in stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 163-169, October.
    7. Deelstra, Griselda, 2000. "Long-Term Returns in Stochastic Interest Rate Models: Applications," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 30(01), pages 123-140, May.
    8. Griselda Deelstra, 2000. "Long-term returns in stochastic interest rate models: applications," ULB Institutional Repository 2013/7590, ULB -- Universite Libre de Bruxelles.
    9. Griselda Deelstra & Freddy Delbaen, 1995. "Long-term returns in stochastic interest rate models: convergence in law," ULB Institutional Repository 2013/7580, ULB -- Universite Libre de Bruxelles.
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    Cited by:

    1. repec:eee:eneeco:v:67:y:2017:i:c:p:496-507 is not listed on IDEAS
    2. Zhang, Zhenzhong & Tong, Jinying & Hu, Liangjian, 2016. "Long-term behavior of stochastic interest rate models with Markov switching," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 320-326.
    3. Novriana Sumarti & Iman Gunadi, 2013. "Reserve Requirement Analysis using a Dynamical System of a Bank based on Monti-Klein model of Bank's Profit Function," Papers 1306.0468, arXiv.org.
    4. Bao, Jianhai & Yuan, Chenggui, 2013. "Long-term behavior of stochastic interest rate models with jumps and memory," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 266-272.

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