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The Ornstein‐Uhlenbeck‐Type Model with a Hybrid Dividend Strategy

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  • Dan Zhu
  • Chuancun Yin

Abstract

We consider the Ornstein‐Uhlenbeck‐type model. We first introduce the model and then find the ordinary differential equations and boundary conditions satisfied by the dividend functions; closed‐form solutions for the dividend value functions are given. We also study the distribution of the time value of ruin. Furthermore, the moments and moment‐generating functions of total discounted dividends until ruin are discussed.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:467948
    DOI: 10.1155/2013/467948
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    References listed on IDEAS

    as
    1. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    2. Peng Li & Chuancun Yin & Ming Zhou, 2013. "The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, November.
    3. Wan, Ning, 2007. "Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 509-523, May.
    4. 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).
    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.
    6. Yin, Chuancun & Wen, Yuzhen, 2013. "An extension of Paulsen–Gjessing’s risk model with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 469-476.
    7. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    8. Hans Gerber & Elias Shiu, 2006. "On Optimal Dividend Strategies In The Compound Poisson Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 76-93.
    9. Chuancun Yin & Yuzhen Wen, 2013. "An extension of Paulsen-Gjessing's risk model with stochastic return on investments," Papers 1302.6757, arXiv.org.
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