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Extended Precise Large Deviations of Random Sums in the Presence of END Structure and Consistent Variation

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  • Shijie Wang
  • Wensheng Wang

Abstract

The study of precise large deviations of random sums is an important topic in insurance and finance. In this paper, extended precise large deviations of random sums in the presence of END structure and consistent variation are investigated. The obtained results extend those of Chen and Zhang (2007) and Chen et al. (2011). As an application, precise large deviations of the prospective‐ loss process of a quasirenewal model are considered.

Suggested Citation

  • Shijie Wang & Wensheng Wang, 2012. "Extended Precise Large Deviations of Random Sums in the Presence of END Structure and Consistent Variation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:436531
    DOI: 10.1155/2012/436531
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    References listed on IDEAS

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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    2. Liu, Yan, 2007. "Precise large deviations for negatively associated random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 181-189, January.
    3. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    4. Shen, Xinmei & Lin, Zhengyan, 2008. "Precise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3222-3229, December.
    5. Baltrunas, Aleksandras & Leipus, Remigijus & Siaulys, Jonas, 2008. "Precise large deviation results for the total claim amount under subexponential claim sizes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1206-1214, August.
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    Cited by:

    1. Aiting Shen, 2013. "Bernstein‐Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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