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Ruin problems in a discrete Markov risk model

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  • Yang, Hu
  • Zhang, Zhimin
  • Lan, Chunmei

Abstract

In this paper, we extend the compound binomial risk model to a Markov dependent model in which the claim occurrence and the claim amount are both regulated by a discrete time Markov process. The explicit expression for the "discounted" joint probability function of the surplus before ruin and the deficit at ruin is derived when the initial surplus u=0, and a recursive formula to calculate such "discounted" joint probability function when the initial surplus u>0 is also obtained.

Suggested Citation

  • Yang, Hu & Zhang, Zhimin & Lan, Chunmei, 2009. "Ruin problems in a discrete Markov risk model," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 21-28, January.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:1:p:21-28
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    References listed on IDEAS

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    1. Willmot, Gordon E., 1993. "Ruin probabilities in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 12(2), pages 133-142, April.
    2. Cheng, Shixue & Gerber, Hans U. & Shiu, Elias S. W., 2000. "Discounted probabilities and ruin theory in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 239-250, May.
    3. Gerber, Hans U., 1988. "Mathematical Fun with the Compound Binomial Process," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 161-168, November.
    4. Albrecher, Hansjorg & Boxma, Onno J., 2005. "On the discounted penalty function in a Markov-dependent risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 650-672, December.
    5. Dickson, David C.M., 1994. "Some Comments on the Compound Binomial Model," ASTIN Bulletin, Cambridge University Press, vol. 24(1), pages 33-45, May.
    6. Shiu, Elias S.W., 1989. "The Probability of Eventual Ruin in the Compound Binomial Model," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 179-190, November.
    7. Cossette, Helene & Landriault, David & Marceau, Etienne, 2004. "Compound binomial risk model in a markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 425-443, October.
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    Cited by:

    1. Ernesto Cruz & Luis Rincón & David J. Santana, 2024. "Ruin Probabilities as Recurrence Sequences in a Discrete-Time Risk Process," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-16, September.

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