Ruin Asymptotic Analysis Of Heavy Tailed Integrated Risk Model Under Dependent Structure

For modern insurance companies,huge claims risk and financial risk are two swords hanging over their heads,which determine the solvency of insurance companies.The ruin probability is an important index to measure solvency,and the characterization of extreme risk is closely related to the heavy-tailed distribution.In addition,the impact of dependent structure on risk can not be underestimated owing to interplay of various of risk factors,.Based on the above references,this paper studies the asymptotic analysis of the finite-time ruin probability under the framework of the heavy tail integrated risk model with dependent structure.This paper mainly studies three aspects:1.Compared with most literatures which only consider single risk,this paper considers the discrete-time risk model of insurance risk and financial risk interaction,that is,the comprehensive risk model.In this model,it is assumed that the dependence of these two risks is characterized by a binary Sarmanov distribution.And the convex combination of the two obeys the strong regular transformation.Under this assumption,we obtain asymptotic estimates and uniform asymptotic estimates of finite-time ruin probability.On this basis,we obtain a generalized form of Brieman’s theorem under a more general dependency structure.It should be noted that the dependencies considered in this paper cover many common copula structures.2.We consider the continuous-time two dimensional risk model with constant interest rate.Multidimensional risk means that insurance companies are running more than one line of business.Compared with one-dimensional risk model,this model has a better guiding significance for practice.In this paper,we assume that the relationship between the claim sizes and their inter-arrival times satisfies the dependent structure proposed by Asimit(2010),and assume that the claim amount follows a local subexponential distribution.Finally,the uniform asymptotic local estimate of the process of two dimensional discounted claims is obtained.Compared with the global estimation,the local estimation of ruin probability is seldom studied,but it has more practical value..From the perspective of quantitative risk management,it is not only necessary to know the likelihood of bankruptcy,but also need to know how much deficit will be caused by bankrupcy.3.We discuss the problem of almost decreasing heavy tailed density.By constructing two examples,it is pointed out that not all density functions in S and L\S.Using these conclusions,the relationship between two definitions of local subexponential distribution is discussed.The results show that there are essential differences in the properties of the local subexponential distribution and the subexponential distribution.