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Precise large deviations for actual aggregate loss process in a dependent compound customer-arrival-based insurance risk model. (English) Zbl 1337.60034

Summary: In this paper, we investigate a dependent compound customer-arrival-based insurance risk model, in which the \(k\)-th customer purchases a random number of insurance contracts, his/her actual individual claim sizes are described as negatively dependent consistently varying-tailed random variables multiplied by a general shot noise function, and the individual customer-arrival process is a Poisson process. We obtain some precise large deviation results for the actual aggregate loss process, which extend and close the gaps of the related results of X.-M. Shen et al. [Stochastic Anal. Appl. 27, No. 5, 1000–1013 (2009; Zbl 1175.60022)].

MSC:

60F10 Large deviations
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
91B30 Risk theory, insurance (MSC2010)

Citations:

Zbl 1175.60022
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References:

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