A Uniform Asymptotic Estimation Of Ruin Probability With Subexponential Innovations

As the core content of risk theory,the problem of ruin probability of insurance companies has been extensively studied,but in order to facilitate the theoretical proof,in previous studies,it is often assumed that financial risks and insurance risks are in-dependent of each other.Even if a small part of the studies considered the relationship between the two kinds of risks,but they often has stringent restrictions on the random variables Y that represents the insurance risk.This paper processed from this point of view,under the premise of a certain dependent structure between financial risk and in-surance risk estimate the asymptotic form of ruin probability of insurance company.At the same time,by adding other constraints,we relaxed the restriction of Y,and assume that it is unbounded.In order to obtain the asymptotic form of the ruin probability,we first proved some properties of the tail probability for product of two random variables.On this basis,we obtain the asymptotic form of the ruin probability under the finite term,and finally extend it to the infinite term and got the asymptotic form of ruin probability of Insurance company.