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The First Passage Time and the Dividend Value Function for One-Dimensional Diffusion Processes between Two Reflecting Barriers

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  • Chuancun Yin
  • Huiqing Wang

Abstract

We consider the general one-dimensional time-homogeneous regular diffusion process between two reflecting barriers. An approach based on the Itô formula with corresponding boundary conditions allows us to derive the differential equations with boundary conditions for the Laplace transform of the first passage time and the value function. As examples, the explicit solutions of them for several popular diffusions are obtained. In addition, some applications to risk theory are considered.

Suggested Citation

  • Chuancun Yin & Huiqing Wang, 2012. "The First Passage Time and the Dividend Value Function for One-Dimensional Diffusion Processes between Two Reflecting Barriers," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-15, October.
    • Handle: RePEc:hin:jnijsa:971212
    DOI: 10.1155/2012/971212
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    Cited by:

    1. Guangli Xu & Xingchun Wang, 2021. "On the Transition Density and First Hitting Time Distributions of the Doubly Skewed CIR Process," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 735-752, September.

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