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Upper bounds for ultimate ruin probabilities in the Sparre Andersen risk model with interest and a nonlinear dividend barrier

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  • Yang, Wenquan
  • Hu, Yijun

Abstract

We consider the classical risk model with constant force of interest and a nonlinear dividend barrier. Lundberg-type inequalities for the ultimate ruin probabilities are derived. The results obtained carry over those of Gerber [Gerber, H.U., 1979. An Introduction to Mathematical Risk Theory. In: Monograph Series, vol. 8. Huebner Foundation, Philadelphia], about a linear dividend barrier without interest, to the case with both interest and a nonlinear dividend barrier. More precise upper bounds for the ultimate ruin probabilities are also given for the special case of exponential claim sizes.

Suggested Citation

  • Yang, Wenquan & Hu, Yijun, 2009. "Upper bounds for ultimate ruin probabilities in the Sparre Andersen risk model with interest and a nonlinear dividend barrier," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 63-69, January.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:1:p:63-69
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    References listed on IDEAS

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    8. 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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