Tail Probabilities Of Multivariate Dependent Risk Models Under Heavy-tailed Risks

This dissertation focuses on discussion of the tail behavior of multivariate dependent risk models under heavy tails.The main result are as follows.Firstly,Consider an m-dimensional renewal risk model,in which the claim sizes{(3_k,k?1}form a sequence of independent,identically distributed and non-negative random vectors with dependent components.The univariate marginal distributions of these vectors have consistently varying tails and finite means.Suppose that the claim sizes and inter-arrival times correspond-ingly form a sequence of independent and identically distributed random pairs,with each pair obeying a dependence structure.Then a precise large deviation for the m-dimensional renewal risk model is obtained.Secondly,an m-dimensional discrete-time risk model with constant interest rate is con-sidered.The insurer is assumed to be exposed to a vector of net losses resulting from m sub-portfolios over each period.The univariate individual net loss is assumed to be in the class of extended regular variation,and the components of net losses are allowed to be generally de-pendent,in the sense that the underlying copula for the net loss vector is multivariate regularly varying.Some asymptotic results for finite-time and infinite-time ruin probabilities are estab-lished.