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Ruin probability in the Cramér-Lundberg model with risky investments

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  • Xiong, Sheng
  • Yang, Wei-Shih

Abstract

We consider the Cramér-Lundberg model with investments in an asset with large volatility, where the premium rate is a bounded nonnegative random function ct and the price of the invested risk asset follows a geometric Brownian motion with drift a and volatility [sigma]>0. It is proved by Pergamenshchikov and Zeitouny that the probability of ruin, [psi](u), is equal to 1, for any initial endowment u>=0, if [rho]:=2a/[sigma]2

Suggested Citation

  • Xiong, Sheng & Yang, Wei-Shih, 2011. "Ruin probability in the Cramér-Lundberg model with risky investments," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1125-1137, May.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:5:p:1125-1137
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    References listed on IDEAS

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    1. Anna Frolova & Serguei Pergamenshchikov & Yuri Kabanov, 2002. "In the insurance business risky investments are dangerous," Finance and Stochastics, Springer, vol. 6(2), pages 227-235.
    2. Pergamenshchikov, Serguei & Zeitouny, Omar, 2006. "Ruin probability in the presence of risky investments," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 267-278, February.
    3. Paulsen, Jostein, 1998. "Sharp conditions for certain ruin in a risk process with stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 135-148, June.
    4. Kalashnikov, Vladimir & Norberg, Ragnar, 2002. "Power tailed ruin probabilities in the presence of risky investments," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 211-228, April.
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