Asymptotic Behaviour For Tail Probabilities Of Dependent Risk Models

In this paper,asymptotic behaviour for tail probabilities of dependent risk models are discussed.The main contents include the following aspects.Firstly,some definitions of classes of heavy-tailed distributions and some properties of the Copula are introduced.Secondly,the ruin probability of a size-dependent renewal risk model is investigated.In the risk model,the random pair of the claim size and its corresponding inter-occurrence time obeys a dependence structure described via the conditional distribution of the inter-occurrence time given the subsequent claim size being large.Under this dependence structure,the tail behaviour of the finite-time ruin probability is studied.Thirdly,the asymptotic behaviour for tail probabilities of randomly weighted sums for twodimensional risk model is focused.Under some mild assumptions,tail probabilities of randomly weighted (?)and their maxima (?) Siare investigated,where (?) is a sequence of independent and identically distributed random vectors,independent of (?) and satisfying mild moment conditions.Further,(?) are generally dependent while the sequences (?) and (?)are independent of each other.