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A risk model with paying dividends and random environment

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

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 2 (April)
    Pages: 717-726

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:717-726

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    Web page: http://www.elsevier.com/locate/inca/505554

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    1. 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, Elsevier, vol. 38(3), pages 529-539, June.
    2. 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, Elsevier, vol. 33(3), pages 551-566, December.
    3. Frostig, Esther, 2005. "The expected time to ruin in a risk process with constant barrier via martingales," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 37(2), pages 216-228, October.
    4. Tan, Jiyang & Yang, Xiangqun, 2006. "The compound binomial model with randomized decisions on paying dividends," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 39(1), pages 1-18, August.
    5. 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, Elsevier, vol. 37(2), pages 324-334, October.
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