Estimations for aggregate amount of claims in a risk model with arbitrary dependence between claim sizes and inter-arrival times

Weiwei Ni; Chenghao Xu; Kaiyong Wang; Weiwei Ni; Chenghao Xu; Kaiyong Wang

doi:10.3934/math.2022976

AIMS Mathematics

2022, Volume 7, Issue 10: 17737-17746. doi: 10.3934/math.2022976

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Research article

Estimations for aggregate amount of claims in a risk model with arbitrary dependence between claim sizes and inter-arrival times

School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, China

Received: 31 May 2022 Revised: 21 July 2022 Accepted: 27 July 2022 Published: 02 August 2022
MSC : 60F10, 91B05, 91G05

This paper considers a compound risk model, in which the individual claim sizes and their inter-arrival times can be arbitrarily dependent. We mainly investigate the claim sizes are extended negatively dependent. When the claim sizes have consistently-varying-tailed distributions, we obtain precise large deviations of the aggregate amount of claims in the above dependent compound risk model.
- precise large deviations,
- compound sums,
- extended negative dependence,
- consistently varying distribution
Citation: Weiwei Ni, Chenghao Xu, Kaiyong Wang. Estimations for aggregate amount of claims in a risk model with arbitrary dependence between claim sizes and inter-arrival times[J]. AIMS Mathematics, 2022, 7(10): 17737-17746. doi: 10.3934/math.2022976

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Abstract

This paper considers a compound risk model, in which the individual claim sizes and their inter-arrival times can be arbitrarily dependent. We mainly investigate the claim sizes are extended negatively dependent. When the claim sizes have consistently-varying-tailed distributions, we obtain precise large deviations of the aggregate amount of claims in the above dependent compound risk model.

References

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