The general principle for precise large deviations of heavy-tailed random sums

2008 ◽  
Vol 78 (6) ◽  
pp. 749-758 ◽  
Author(s):  
Jianxi Lin
Keyword(s):  
Large Deviations ◽  
General Principle ◽  
Random Sums ◽  
Precise Large Deviations ◽  
Heavy Tailed

scholarly journals Precise Large Deviations for Random Sums of END Random Variables with Dominated Variation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yu Chen ◽  
Zhihui Qu
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Random Sums ◽  
Tail Probabilities ◽  
Precise Large Deviations ◽  
Surplus Process ◽  
End Random Variables ◽  
Renewal Risk

We investigate the precise large deviations for random sums of extended negatively dependent random variables with long and dominatedly varying tails. We find out that the asymptotic behavior of precise large deviations of random sums is insensitive to the extended negative dependence. We apply the results to a generalized dependent compound renewal risk model including premium process and claim process and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.

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

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shijie Wang ◽  
Wensheng Wang
Keyword(s):  
Large Deviations ◽  
Random Sums ◽  
Precise Large Deviations ◽  
Consistent Variation ◽  
Loss Process

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.

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

2007 ◽  
Vol 44 (04) ◽  
pp. 889-900 ◽  
Author(s):  
Shijie Wang ◽  
Wensheng Wang
Keyword(s):  
Large Deviations ◽  
Partial Sums ◽  
Counting Processes ◽  
Insurance Company ◽  
Random Sums ◽  
Risk Models ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Insurance Contracts ◽  
Claim Number

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

scholarly journals Precise Large Deviations of Aggregate Claims with Dominated Variation in Dependent Multi-Risk Models

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shijie Wang ◽  
Xuejun Wang ◽  
Wensheng Wang
Keyword(s):  
Large Deviations ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Random Sums ◽  
Risk Models ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Dominated Variation ◽  
Random Array ◽  
Aggregate Claims

We consider a dependent multirisk model in insurance, where all the claims constitute a linearly extended negatively orthant dependent (LENOD) random array, and then upper and lower bounds for precise large deviations of nonrandom and random sums of random variables with dominated variation are investigated. The obtained results extend some related existing ones.

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

2007 ◽  
Vol 44 (4) ◽  
pp. 889-900 ◽  
Author(s):  
Shijie Wang ◽  
Wensheng Wang
Keyword(s):  
Large Deviations ◽  
Partial Sums ◽  
Counting Processes ◽  
Insurance Company ◽  
Random Sums ◽  
Risk Models ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Insurance Contracts ◽  
Claim Number

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.

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