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Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model

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  • Tang, Qihe
  • Wang, Guojing
  • Yuen, Kam C.

Abstract

Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same asymptotic formula holds for the finite-time and infinite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability.

Suggested Citation

  • Tang, Qihe & Wang, Guojing & Yuen, Kam C., 2010. "Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 362-370, April.
    • Handle: RePEc:eee:insuma:v:46:y:2010:i:2:p:362-370
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    References listed on IDEAS

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    Cited by:

    1. Guo, Fenglong, 2022. "Ruin probability of a continuous-time model with dependence between insurance and financial risks caused by systematic factors," Applied Mathematics and Computation, Elsevier, vol. 413(C).
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    3. Fu, Ke-Ang & Ng, Cheuk Yin Andrew, 2014. "Asymptotics for the ruin probability of a time-dependent renewal risk model with geometric Lévy process investment returns and dominatedly-varying-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 80-87.
    4. Li, Jinzhu, 2016. "Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 195-204.
    5. Ming Cheng & Dingcheng Wang, 2023. "Uniform Asymptotic Estimate for the Ruin Probability in a Renewal Risk Model with Cox–Ingersoll–Ross Returns," Mathematics, MDPI, vol. 11(5), pages 1-10, March.
    6. Zhang, Yuanyuan & Wang, Wensheng, 2012. "Ruin probabilities of a bidimensional risk model with investment," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 130-138.
    7. Cheng, Ming & Konstantinides, Dimitrios G. & Wang, Dingcheng, 2022. "Uniform asymptotic estimates in a time-dependent risk model with general investment returns and multivariate regularly varying claims," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    8. Jiang, Tao & Cui, Sheng & Ming, Ruixing, 2015. "Large deviations for the stochastic present value of aggregate claims in the renewal risk model," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 83-91.

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