Approximations For Tail Probabilities Of Dependent Risk Models

In this paper, approximations for tail probabilities of dependent risk models are discussed. The main contents include the following aspects.Firstly, some definitions of class of heavy-tailed distributions and some properties of the Copula are introduced.Secondly, aiming at precise large deviations for multi-dimensional risk models, we provide mail results and by using software R, contrapose the numerical results to illustrate the reliability of the theorems. Also on the basis of assumptions, precise large deviations for both the partial sums Sn�'=∑i=1nXi�' and the random sums SN(t)�'=∑i=1N(t)Xi�' are investigated.Thirdly, aiming at approximation for the tail probability of randomly weighted sums for two-dimensional risk models. Under some mild assumptions, tail probabilities of randomly weighted sums ∑k=1n(?)kXk�' and their maxima Mn�'=max1≤i≤nSi�'  are investigated, where {Xk�'= (X1,k,X2,k)T, k≥1} is a sequence of independent and identically distributed random vectors with common marginal distributions having extended regularly varying tails, and {(?)k,k≥1} is a sequence of dependent random variables, independent of {Xk, k≥1},Finally, the primary work of this paper is summarized.