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A risk model with paying dividends and random environment

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  • Kim, Bara
  • Kim, Hwa-Sung
  • Kim, Jeongsim

Abstract

We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given.

Suggested Citation

  • Kim, Bara & Kim, Hwa-Sung & Kim, Jeongsim, 2008. "A risk model with paying dividends and random environment," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 717-726, April.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:717-726
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    References listed on IDEAS

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    1. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 324-334, October.
    2. Frostig, Esther, 2005. "The expected time to ruin in a risk process with constant barrier via martingales," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 216-228, October.
    3. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    4. Tan, Jiyang & Yang, Xiangqun, 2006. "The compound binomial model with randomized decisions on paying dividends," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 1-18, August.
    5. Li, Shuanming & Dickson, David C.M., 2006. "The maximum surplus before ruin in an Erlang(n) risk process and related problems," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 529-539, June.
    6. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Cited by:

    1. Steve Drekic & Ana Maria Mera, 2011. "Ruin Analysis of a Threshold Strategy in a Discrete-Time Sparre Andersen Model," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 723-747, December.

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