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The Exit Time and the Dividend Value Function for One‐Dimensional Diffusion Processes

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  • Peng Li
  • Chuancun Yin
  • Ming Zhou

Abstract

We investigate the exit times from an interval for a general one‐dimensional time‐homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. Then, as some examples, we solve the closed‐form expression of the Laplace transform of the exit times for several popular diffusions, which are commonly used in modelling of finance and insurance market. Most interestingly, as the applications of the exit times, we create the connect between the dividend value function and the Laplace transform of the exit times. Both the barrier and threshold dividend value function are clearly expressed in terms of the Laplace transform of the exit times.

Suggested Citation

  • Peng Li & Chuancun Yin & Ming Zhou, 2013. "The Exit Time and the Dividend Value Function for One‐Dimensional Diffusion Processes," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:675202
    DOI: 10.1155/2013/675202
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    References listed on IDEAS

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    5. Jun Cai & Hans Gerber & Hailiang Yang, 2006. "Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 94-108.
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    Cited by:

    1. Dan Zhu & Chuancun Yin, 2013. "The Ornstein‐Uhlenbeck‐Type Model with a Hybrid Dividend Strategy," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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