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On a risk model with debit interest and dividend payments

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  • Yuen, Kam-Chuen
  • Zhou, Ming
  • Guo, Junyi

Abstract

We consider the compound Poisson risk model with debit interest and dividend payments. The model assumes that the company is allowed to borrow at some debit interest rate when the surplus turns negative, and that the premium incomes are paid out as dividends to shareholders when the surplus reaches a horizontal barrier of level b. We first derive integro-differential equations for the expected discounted value of all dividends until absolute ruin, Vb(u), which is twice continuously differentiable. In the case of exponential claim amounts, we obtain explicit expressions for Vb(u) and the optimal barrier b* which maximizes Vb(u). We then perform a similar study for the Gerber-Shiu expected discounted penalty function. Again, when claims are exponentially distributed, we are able to find explicit expressions for the joint distribution of the surplus just prior to absolute ruin and the deficit at absolute ruin, which is a special case of the Gerber-Shiu function.

Suggested Citation

  • Yuen, Kam-Chuen & Zhou, Ming & Guo, Junyi, 2008. "On a risk model with debit interest and dividend payments," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2426-2432, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2426-2432
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    References listed on IDEAS

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    1. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    2. Yuen, Kam C. & Wang, Guojing & Li, Wai K., 2007. "The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 104-112, January.
    3. Hans Gerber & Hailiang Yang, 2007. "Absolute Ruin Probabilities in a Jump Diffusion Risk Model with Investment," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 159-169.
    4. Paulsen, Jostein & Gjessing, Hakon K., 1997. "Optimal choice of dividend barriers for a risk process with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 215-223, October.
    5. Jun Cai & Hans Gerber & Hailiang Yang, 2006. "Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 94-108.
    6. Zhang, Chunsheng & Wu, Rong, 1999. "On the distribution of the surplus of the D-E model prior to and at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 309-321, May.
    7. Gerber, Hans U. & Shiu, Elias S.W. & Smith, Nathaniel, 2008. "Methods for estimating the optimal dividend barrier and the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 243-254, February.
    8. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
    9. 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. Li, Manman & Liu, Zaiming, 2012. "Regulated absolute ruin problem with interest structure and linear dividend barrier," Economic Modelling, Elsevier, vol. 29(5), pages 1786-1792.
    2. Zhang, Yuanyuan & Wang, Wensheng, 2012. "Ruin probabilities of a bidimensional risk model with investment," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 130-138.
    3. Yin, Chuancun & Yuen, Kam Chuen, 2011. "Optimality of the threshold dividend strategy for the compound Poisson model," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1841-1846.
    4. Zhou, Ming & Yuen, Kam C., 2012. "Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle," Economic Modelling, Elsevier, vol. 29(2), pages 198-207.

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