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 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.

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.

Precise large deviations for sums of random variables with consistently varying tails

2004 ◽  
Vol 41 (01) ◽  
pp. 93-107 ◽  
Author(s):  
Kai W. Ng ◽  
Qihe Tang ◽  
Jia-An Yan ◽  
Hailiang Yang
Keyword(s):  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Tail Probability ◽  
Arrival Process ◽  
Partial Sums ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Doubly Stochastic ◽  
Common Distribution Function

Let {X k , k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums S n and the random sums S N(t), where N(·) is a counting process independent of the sequence {X k , k ≥ 1}. The obtained results improve some related classical ones. Applications to a risk model with negatively associated claim occurrences and to a risk model with a doubly stochastic arrival process (extended Cox process) are proposed.

Precise large deviations for sums of random variables with consistently varying tails

2004 ◽  
Vol 41 (1) ◽  
pp. 93-107 ◽  
Author(s):  
Kai W. Ng ◽  
Qihe Tang ◽  
Jia-An Yan ◽  
Hailiang Yang
Keyword(s):  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Tail Probability ◽  
Arrival Process ◽  
Partial Sums ◽  
Precise Large Deviations ◽  
Sums Of Random Variables ◽  
Doubly Stochastic ◽  
Common Distribution Function

Let {Xk, k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums Sn and the random sums SN(t), where N(·) is a counting process independent of the sequence {Xk, k ≥ 1}. The obtained results improve some related classical ones. Applications to a risk model with negatively associated claim occurrences and to a risk model with a doubly stochastic arrival process (extended Cox process) are proposed.

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.

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