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Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-Risk Models

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Shijie Wang  and
Wensheng Wang
Shijie Wang*
Affiliation:
East China Normal University and Anhui University
Wensheng Wang*
Affiliation:
East China Normal University
*
∗Postal address: Department of Statistics, East China Normal University, Shanghai 200062, P. R. China.
∗Postal address: Department of Statistics, East China Normal University, Shanghai 200062, P. R. China.
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Abstract

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Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {Xij, j ≥ 1}, i = 1,…,k. In this paper we investigate large deviations for both partial sums S(k; n1,…,nk) = ∑i=1k ∑j=1niXij and random sums S(k; t) = ∑i=1k ∑j=1Ni (t)Xij, where Ni(t), i = 1,…,k, are counting processes for the claim number. The obtained results extend some related classical results.

Keywords

Large deviationloss processconsistently varying tailsums of random variables

MSC classification

Secondary: 60F10: Large deviations 60F05: Central limit and other weak theorems 60G50: Sums of independent random variables; random walks
Type
Research Papers
Information
Journal of Applied Probability , Volume 44 , Issue 4 , December 2007 , pp. 889 - 900
Copyright
Copyright © Applied Probability Trust 2007 

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