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The Probability of Eventual Ruin in the Compound Binomial Model

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  • Shiu, Elias S.W.

Abstract

This paper derives several formulas for the probability of eventual ruin in a discrete-time model. In this model, the number of claims process is assumed to be binomial. The claim amounts, premium rate and initial surplus are assumed to be integer-valued.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:19:y:1989:i:02:p:179-190_00
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    Citations

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    Cited by:

    1. Kam Pui Wat & Kam Chuen Yuen & Wai Keung Li & Xueyuan Wu, 2018. "On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends," Risks, MDPI, vol. 6(1), pages 1-13, January.
    2. Dutang, C. & Lefèvre, C. & Loisel, S., 2013. "On an asymptotic rule A+B/u for ultimate ruin probabilities under dependence by mixing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 774-785.
    3. Bao, Zhenhua & Song, Lixin & Liu, He, 2013. "A note on the inflated-parameter binomial distribution," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1911-1914.
    4. Cossette, Helene & Landriault, David & Marceau, Etienne, 2006. "Ruin probabilities in the discrete time renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 309-323, April.
    5. 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.
    6. Andrius Grigutis & Jonas Šiaulys, 2020. "Ultimate Time Survival Probability in Three-Risk Discrete Time Risk Model," Mathematics, MDPI, vol. 8(2), pages 1-30, January.
    7. Cossette, Hélène & Marceau, Etienne & Mtalai, Itre & Veilleux, Déry, 2018. "Dependent risk models with Archimedean copulas: A computational strategy based on common mixtures and applications," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 53-71.
    8. Cossette, Helene & Landriault, David & Marceau, Etienne, 2004. "Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 449-466, June.
    9. Chen, Mi & Yuen, Kam Chuen & Guo, Junyi, 2014. "Survival probabilities in a discrete semi-Markov risk model," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 205-215.
    10. De Vylder, F. & Marceau, E., 1996. "The numerical solution of the Schmitter problems: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 1-18, December.
    11. Liu, Guoxin & Wang, Ying & Zhang, Bei, 2005. "Ruin probability in the continuous-time compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 303-316, June.
    12. Marceau, Etienne, 2009. "On the discrete-time compound renewal risk model with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 245-259, April.
    13. Liu, Guoxin & Zhao, Jinyan, 2007. "Joint distributions of some actuarial random vectors in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 95-103, January.
    14. Cossette, Hélène & Marceau, Etienne & Trufin, Julien & Zuyderhoff, Pierre, 2020. "Ruin-based risk measures in discrete-time risk models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 246-261.
    15. Willmot, Gordon E. & Cai, Jun, 2001. "Aging and other distributional properties of discrete compound geometric distributions," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 361-379, June.
    16. Jae-Kyung Woo & Haibo Liu, 2018. "Discounted Aggregate Claim Costs Until Ruin in the Discrete-Time Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1285-1318, December.
    17. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
    18. Stanisław Heilpern, 2010. "Dependent discrete risk processes - calculation of the probability of ruin," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 20(2), pages 59-76.
    19. Yuen, K. C. & Guo, J. Y., 2001. "Ruin probabilities for time-correlated claims in the compound binomial model," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 47-57, August.
    20. 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.
    21. 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.

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