Asymptotic Approximation Of Tail Probabilities For Heavy-tailed Risk Models Under Two Types Of Dependence Structures

In actuarial science,risk theory has always been a hot topic,and one of the most im-portant issues is the gradual estimation of ruin probability.In fact,the estimate of ruin probability is the study of tail probability.This paper mainly considers asymp-totic approximation of tail probabilities under the different dependence structure of the main claims,which belong to heavy tailed distributions.Firstly,consider the nonstan-dard updating model with constant interest force,in which the random variables of the main claims satisfy the CLWD(conditionally linearly wide dependent)and the claim arrival time interval is independent and identically distributed.When the main claims belong to D?(?)(the intersection of dominatedly varying tailed distribution and long tailed distribution),we obtain an asymptotic formula of tail probabilities of discount-ed aggregate claims,which holds locally uniform for all time horizon within a finite interval,particularly,when the claim sizes are further restricted to be C(consistent-ly varying tailed distribution),we show that asymptotic formula of tail probabilities is globally uniform for all time horizon within a infinite interval.Secondly,consider main claim randomly variables belong to S(subexponential distribution)and satisfy a class of wide dependence structure.The other random variables are nonnegative arbitrari-ly dependence and bound.we obtain asymptotic approximation of tail probabilities of finite randomly weighted sums,particularly,when the main claim randomly variables are further restricted to be C,we show that asymptotic formula of tail probabilities is infinite randomly weight sums.Finally,we obtained results on randomly weighted sums are applied to estimating the finite-time ruin probabilities in a discrete-time risk model with both insurance and financial risk.