Precise Large Deviations for Sums of Random Variables with Consistent Variation in Dependent Multi-Risk Models

Abstract

Abstract In this article, we set up dependent multi-risk models in insurance, where all the claims constitute ENA (extended negatively associated) random arrays. Precise large deviations for non random sums and random sums of the dependent multi-risk models with ENA structure and consistent variation are investigated. The obtained results extend those of Wang and Wang (Citation2007), Liu (Citation2009), and Chen et al. (Citation2011). Keywords: Consistent variationExtended negative dependenceLarge deviationMulti-risk modelRandom arrayMathematics Subject Classification: 60F1060F0560G50 Acknowledgments The author would like to thank the referees for their constructive and insightful comments and suggestions that greatly improved the article. The author thanks an anonymous referee who kindly pointed out a mistake in the proofs of the main results. This work was partially supported by NSFC grant 11071076 and 11226207, the Talents Youth Fund of Anhui Province Universities (2011SQRL012ZD), the Project Sponsored by the Doctoral Scientific Research Foundation of Anhui University, and the 211 Project of Anhui University (2009QN020B).