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Integrated insurance risk models with exponential Lévy investment

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  • Klüppelberg, Claudia
  • Kostadinova, Radostina

Abstract

We consider an insurance risk model for the cashflow of an insurance company, which invests its reserve into a portfolio consisting of risky and riskless assets. The price of the risky asset is modeled by an exponential Lévy process. We derive the integrated risk process and the corresponding discounted net loss process. We calculate certain quantities as characteristic functions and moments. We also show under weak conditions stationarity of the discounted net loss process and derive the left and right tail behavior of the model. Our results show that the model carries a high risk, which may originate either from large insurance claims or from the risky investment.

Suggested Citation

  • Klüppelberg, Claudia & Kostadinova, Radostina, 2008. "Integrated insurance risk models with exponential Lévy investment," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 560-577, April.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:560-577
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    References listed on IDEAS

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    Cited by:

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    3. Henrik Hult & Filip Lindskog, 2011. "Ruin probabilities under general investments and heavy-tailed claims," Finance and Stochastics, Springer, vol. 15(2), pages 243-265, June.
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    6. Chen, Yiqing & Yuan, Zhongyi, 2017. "A revisit to ruin probabilities in the presence of heavy-tailed insurance and financial risks," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 75-81.
    7. Li, Ping & Zhao, Wu & Zhou, Wei, 2015. "Ruin probabilities and optimal investment when the stock price follows an exponential Lévy process," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 1030-1045.

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