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

Assume that there are two types of insurance contracts in an insurance company. Theith 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 = 1X2jand random difference ∑N1(t)j = 1X1j− ∑N2(t)j = 1X2j, whereni(t) are positive integer functions ast→ ∞,ni(t) → ∞,i= 1, 2.Ni(t),i= 1, 2 are counting processes for the claim number. [ABSTRACT FROM AUTHOR]