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Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation

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Abstract

The study of precise large deviations for random sums is an important topic in insurance and finance. In this paper, we extend recent results of Tang (Electron J Probab 11(4):107–120, 2006) and Liu (Stat Probab Lett 79(9):1290–1298, 2009) to random sums in various situations. In particular, we establish a precise large deviation result for a nonstandard renewal risk model in which innovations, modelled as real-valued random variables, are negatively dependent with common consistently-varying-tailed distribution, and their inter-arrival times are also negatively dependent.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Liverpool, Liverpool, L69 7ZL, UK

    Yiqing Chen

  2. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong

    Kam C. Yuen & Kai W. Ng

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  1. Yiqing Chen
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  2. Kam C. Yuen
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  3. Kai W. Ng
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Correspondence to Yiqing Chen.

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Chen, Y., Yuen, K.C. & Ng, K.W. Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation. Methodol Comput Appl Probab 13, 821–833 (2011). https://doi.org/10.1007/s11009-010-9194-7

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  • DOI: https://doi.org/10.1007/s11009-010-9194-7

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