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Large deviations for the stochastic present value of aggregate claims in the renewal risk model

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  • Jiang, Tao
  • Cui, Sheng
  • Ming, Ruixing

Abstract

In insurance, if the insurer continuously invests her wealth in risk-free and risky assets, then the price process of the investment portfolio can be described as a geometric Lévy process. People always are interested in estimating the tail distribution of the stochastic present value of aggregate claims. In this paper, the large deviations for the stochastic present value of aggregate claims, when the claim size distribution is of Pareto type with finite variance, are obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:101:y:2015:i:c:p:83-91
    DOI: 10.1016/j.spl.2015.02.020
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    References listed on IDEAS

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    1. 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.
    2. Tang, Qihe & Su, Chun & Jiang, Tao & Zhang, Jinsong, 2001. "Large deviations for heavy-tailed random sums in compound renewal model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 91-100, March.
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    Cited by:

    1. Gao, Qingwu & Lin, Jia’nan & Liu, Xijun, 2023. "Large deviations of aggregate amount of claims in compound risk model with arbitrary dependence between claim sizes and waiting times," Statistics & Probability Letters, Elsevier, vol. 197(C).

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