Release Time:2019-03-09  Hits:

Indexed by: Journal Papers

Date of Publication: 2016-01-17

Journal: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

Included Journals: EI、SCIE

Volume: 45

Issue: 2

Page Number: 291-306

ISSN: 0361-0926

Key Words: Consistently varying tailed distributions; Difference of two sums of heavy-tailed random variables; Heavy-tailed; Precise large deviations

Abstract: Assume that there are two types of insurance contracts in an insurance company. The ith related claims are denoted by {X-ij, j >= 1}, i = 1, 2. In this paper, we investigate large deviations for the difference Sigma(n1(t))(j=1) X-1j - Sigma(n2(t))(j = 1) X-2j and random difference Sigma X-N1(t)(j = 1)1j - Sigma(N2(t))(j = 1) X-2j, where n(i)(t) are positive integer functions as t -> infinity, n(i)(t) ->infinity, i = 1, 2. N-i(t), i = 1, 2 are counting processes for the claim number.