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

  • Yang, Wenquan
  • Hu, Yijun
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    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.

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

    Volume (Year): 79 (2009)
    Issue (Month): 1 (January)
    Pages: 63-69

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    Handle: RePEc:eee:stapro:v:79:y:2009:i:1:p:63-69
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    1. Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
    2. Sundt, Bjorn & Teugels, Jozef L., 1997. "The adjustment function in ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 85-94, April.
    3. Kalashnikov, Vladimir & Konstantinides, Dimitrios, 2000. "Ruin under interest force and subexponential claims: a simple treatment," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 145-149, August.
    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. Cai, Jun, 2004. "Ruin probabilities and penalty functions with stochastic rates of interest," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 53-78, July.
    6. 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.
    7. Cai, Jun & Dickson, David C. M., 2002. "On the expected discounted penalty function at ruin of a surplus process with interest," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 389-404, June.
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