Estimation For Ruin Probabilities Of Risk Models With Main Claims And By-claims

This paper gives some estimations for some quantities of a risk model with heavy-tailed main claims and by-claims.For the risk models with main claims,two types of dependent risk models are investigated.One dependent risk model is that the claims are dependent and there exists a size-dependent structure between the claims and the inter-arrival times.When the claims are WOD,the precise large deviations of aggregate claims are obtained for the multiple delayed inter-arrival times.The other dependent risk model is that there is a time-dependent structure between the claims and the inter-arrival times.For this risk model we mainly consider the income of the investment portfolio is a geometric Le?vy process and investigate the influence of perturbation on ruin probabilities.When the claims have dominated varying tails,the asymptotics of finite-time ruin probability have been given.For the risk model with by-claims,the risk model with a constant interest rate are discussed.When the main claims and the by-claims have subexponential distributions,the effects of the perturbation on ruin probabilities have been investigated and the asymptotics of the finite-time ruin probabilities have been presented.