Precise large deviations for the difference of two sums of END random variables with heavy tails.

Assume that there are two types of insurance contracts in an insurance company, and theith related claims are denoted by {Xij,j⩾ 1},i= 1, 2. In this article, the asymptotic behaviors of precise large deviations for non random difference ∑n1(t)j = 1X1j− ∑n2(t)j = 1X2jand random difference ∑N1(t)j = 1X1j− ∑N2(t)j = 1X2jare investigated, and under several assumptions, some corresponding asymptotic formulas are obtained. [ABSTRACT FROM PUBLISHER]