Abstract
In this paper, we obtain the weakly asymptotic formulas of the tail probabilities of randomly weighted sums and their maximum of dominated varying-tailed random variables under a general conditional dependence structure, where the corresponding random weights can take values in the whole real space. The obtained results extend and improve some existing ones. An application of the weakly asymptotic formulas is proposed to estimate the ruin probability in a discrete-time risk model.
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Acknowledgements
The authors would like to thank two anonymous referees for their valuable comments which can improve the presentation and the quality of the earlier version of this paper. The research was supported by the National Natural Science Foundation of China (NOs.11501295 and 11871289), the Postdoctoral Science Foundation of China (NO.2015M580415), the Natural Science Foundation of Jiangsu Province of China (NO.BK20151459), the Social Science Foundation of Jiangsu Province of China (NO.16GLC006), the Postdoctoral Science Foundation of Jiangsu Province of China (NO.1501004B), the Natural Science Research of Jiangsu Higher Education Institutions of China (NO.19KJB110003), and Qing-Lan Project of Jiangsu Province.
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Gao, Q., Liu, X. Randomly weighted sums of conditionally dependent and dominated varying-tailed increments with application to ruin theory. J. Korean Stat. Soc. 49, 596–624 (2020). https://doi.org/10.1007/s42952-019-00031-x
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DOI: https://doi.org/10.1007/s42952-019-00031-x