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

Abstract

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 . . , k, are counting processes for the claim number. The obtained results extend some related classical results.

Precise Large Deviations for Subexponential Distributions in a Multi Risk Model

“…The multi-risk model was firstly introduced in Wang and Wang (2007) and has arisen from the following construction: Let {X i,j , j ≥ 1}, i = 1, 2, . .…”

“…Under mild conditions, we extend the previous results from the paper Denisov et al (2010) to asymptotics that are valid uniformly over some time interval. Finally, we apply the main result on the multi-risk model introduced by Wang and Wang (2007). …”

Precise deviations for Cox processes with a shot noise intensity

“…It is worth mentioning that the results of precise large deviations for random sums are particulary useful for evaluation of some risk measures such as conditional tail expectation and value at risk of aggregate claims of a large insurance portfolio; see McNeil et al (2005) for a review of risk measures. Wang and Wang (2007) investigated precise large deviations of multi-risk models.…”

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

“…In consideration of insurance reality, some researchers have begun to focus on the precise large deviations of multirisk models in the past few years. See S. Wang and W. Wang [17], Lu [18,19], He at al. [20], and S. J. Wang and W. S. Wang [21], among others.…”

“…[20], and S. J. Wang and W. S. Wang [21], among others. For convenience of representation, we adopt the notations of S. Wang and W. Wang [17]. Assume that the insurer manages types of insurance contracts at the same time, where is any fixed positive integer.…”