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Second order asymptotics for ruin probabilities in a renewal risk model with heavy-tailed claims

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  • Lin, Jianxi

Abstract

In this paper, we establish the second order asymptotics of ruin probabilities of a renewal risk model under the condition that the equilibrium distribution of claim sizes belongs to a rather general heavy-tailed distribution subclass—the class of second order subexponential distributions with finite mean. What is more, this requirement is proved to be necessary. Furthermore, a rather general sufficient condition on the claim size distribution itself is presented. Moreover, an extension to the case of random walk is also included.

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  • Lin, Jianxi, 2012. "Second order asymptotics for ruin probabilities in a renewal risk model with heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 422-429.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:422-429
    DOI: 10.1016/j.insmatheco.2012.07.001
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    References listed on IDEAS

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    8. Barbe, Ph. & McCormick, W.P. & Zhang, C., 2007. "Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1835-1847, December.
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    Cited by:

    1. Peng, Zuoxiang & Liao, Xin, 2015. "Second-order asymptotics for convolution of distributions with light tails," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 199-208.
    2. Lin, Jianxi, 2019. "Second order tail approximation for the maxima of randomly weighted sums with applications to ruin theory and numerical examples," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 37-47.
    3. Yang Yang & Shuang Liu & Kam Chuen Yuen, 2022. "Second-Order Tail Behavior for Stochastic Discounted Value of Aggregate Net Losses in a Discrete-Time Risk Model," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2600-2621, December.

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