Precise Large Deviations For Two-dimensional Risk Model

Precise large deviations for sums of two-dimensional random vectors are discussed. The main contents include the following aspects.Firstly, some definitions of the large deviations and and properties of the copula are intro-duced.Secondly, the assumptions for two-dimensional are proposed. Copula theory is presented to describe dependence of two-dimensional risk model, and meeting the hypothetical example is given.Thirdly, under some mild assumptions of chapter two, precise large deviations for both the partial sums Sn=∑k=1nXk and the random sums SN(t)=∑k=1N(t)Xk are investigated, where N(t) is a counting process independent of the sequence {Xk,k≥1}.{Xk,k≥1} be a sequence of independent identically distributed non-negative random vectors with common marginal distributions F1, F2having extended regularly varying tails, joint distribution function F1,2and finite mean μ=EX1.Finally, the practical application of theorems are presented.