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Precise large deviations for actual aggregate loss process in a dependent compound customer-arrival-based insurance risk model |
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| Authors: | Yang Yang Remigijus Leipus² Jonas Šiaulys² |
| Institution: | 1. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 210029, PR China 2. School of Economics and Management, Southeast University, Nanjing, 210096, PR China 3. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania 4. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania |
| Abstract: | In this paper, we investigate a dependent compound customer-arrival-based insurance risk model, in which the kth 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 Shen et al. X. Shen, Z. Lin, and Y. Zhang, Precise large deviations for the actual aggregate loss process, Stoch. Anal. Appl., 27:1000–1013, 2009]. |
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