Precise large deviation for the difference of two sums of random variables

Dawei Lu, Lixin Song and Xiaohu Wang

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 2, 291-306

Abstract: Assume that there are two types of insurance contracts in an insurance company. The ith related claims are denoted by {Xij, j ⩾ 1}, i = 1, 2. In this paper, we investigate large deviations for the difference ∑n1(t)j = 1X1j − ∑n2(t)j = 1X2j and random difference ∑N1(t)j = 1X1j − ∑N2(t)j = 1X2j, where ni(t) are positive integer functions as t → ∞, ni(t) → ∞, i = 1, 2. Ni(t), i = 1, 2 are counting processes for the claim number.

Date: 2016
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DOI: 10.1080/03610926.2013.804568

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