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The Compound Binomial Risk Model with Randomly Charging Premiums and Paying Dividends to Shareholders

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  • Xiong Wang
  • Lei He

Abstract

Based on characteristics of the nonlife joint‐stock insurance company, this paper presents a compound binomial risk model that randomizes the premium income on unit time and sets the threshold x for paying dividends to shareholders. In this model, the insurance company obtains the insurance policy in unit time with probability p0 and pays dividends to shareholders with probability p1 when the surplus is no less than x. We then derive the recursive formulas of the expected discounted penalty function and the asymptotic estimate for it. And we will derive the recursive formulas and asymptotic estimates for the ruin probability and the distribution function of the deficit at ruin. The numerical examples have been shown to illustrate the accuracy of the asymptotic estimations.

Suggested Citation

  • Xiong Wang & Lei He, 2013. "The Compound Binomial Risk Model with Randomly Charging Premiums and Paying Dividends to Shareholders," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:748204
    DOI: 10.1155/2013/748204
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    References listed on IDEAS

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    1. He, Lei & Yang, Xiangqun, 2010. "The compound binomial model with randomly paying dividends to shareholders and policyholders," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 443-449, June.
    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. 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.
    4. David Landriault, 2008. "Randomized dividends in the compound binomial model with a general premium rate," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2008(1), pages 1-15.
    5. Héléne Cossette & David Landriault & Étienne Marceau, 2003. "Ruin Probabilities in the Compound Markov Binomial Model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2003(4), pages 301-323.
    6. Xiao, Yuntao & Guo, Junyi, 2007. "The compound binomial risk model with time-correlated claims," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 124-133, July.
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