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Precise large deviations of aggregate claim amount in a dependent renewal risk model

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  • Xijun Liu
  • Changjun Yu
  • Qingwu Gao

Abstract

In this paper, we consider a dependent risk model, in which the claim sizes are ofdependence structure, their inter-arrival times are independent, identically distributed (i.i.d.), and the claim size and its corresponding inter-arrival time satisfy a certain dependence structure described via the conditional distribution of the inter-arrival time given the subsequent claim size being large. We obtain the asymptotics of the lower and upper bounds of precise large deviations for the aggregate amount of claims, which holds uniformly for all x in an infinite interval of t.

Suggested Citation

  • Xijun Liu & Changjun Yu & Qingwu Gao, 2017. "Precise large deviations of aggregate claim amount in a dependent renewal risk model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2354-2363, March.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:5:p:2354-2363
    DOI: 10.1080/03610926.2015.1044666
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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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