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On a risk model with debit interest and dividend payments

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

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.

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Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 78 (2008)
Issue (Month): 15 (October)
Pages: 2426-2432

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Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2426-2432
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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  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.
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