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.

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.

scholarly journals Precise large deviations for the aggregate claims in a dependent compound renewal risk model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Kaiyong Wang ◽  
Lamei Chen
Keyword(s):  
Large Deviations ◽  
Risk Model ◽  
Tail Probability ◽  
Dependence Structure ◽  
Precise Large Deviations ◽  
Renewal Risk Model ◽  
Aggregate Claims ◽  
Renewal Risk ◽  
Distribution Class ◽  
Compound Renewal Risk Model

Abstract We consider a dependent compound renewal risk model, where the interarrival times of accidents and the claim numbers follow a dependence structure characterized by a conditional tail probability and the claim sizes have a pairwise negatively quadrant dependence structure or a related dependence structure with the upper tail asymptotical dependence structure. When the distributions of the claim sizes belong to the dominated variation distribution class, we give the asymptotic lower and upper bounds for the precise large deviations of the aggregate claims.

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.

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