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Moments of the first passage time of one-dimensional diffusion with two-sided barriers

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  • Wang, Huiqing
  • Yin, Chuancun

Abstract

We consider a one-dimensional time-homogeneous regular diffusion between two constant elastic barriers as well as the special cases with pure absorbing and/or reflecting barriers. We derive the recurrence relations for moments of the first passage time. As examples, we consider several popular diffusions. Finally, some applications to risk theory are considered.

Suggested Citation

  • Wang, Huiqing & Yin, Chuancun, 2008. "Moments of the first passage time of one-dimensional diffusion with two-sided barriers," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3373-3380, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3373-3380
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    References listed on IDEAS

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    1. Hans Gerber & Elias Shiu, 2004. "Optimal Dividends," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(1), pages 1-20.
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    4. Saphores, Jean-Daniel M., 2005. "The density of bounded diffusions," Economics Letters, Elsevier, vol. 86(1), pages 87-93, January.
    5. Ditlevsen, Susanne, 2007. "A result on the first-passage time of an Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1744-1749, December.
    6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
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    Cited by:

    1. Cabral-García, Gabriela de Jesús & Villa-Morales, José, 2024. "Conditional moments of the first-passage time of a crowed population," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    2. Kristoffer Lindensjö & Filip Lindskog, 2020. "Optimal dividends and capital injection under dividend restrictions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 461-487, December.

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