Extension Research On The Ruin Probability Of Heavy-tailed Risk Model

Ruin probability is an important research index in risk theory.Different from the classical risk model which studies the small claims,the heavy-tailed distribution can depict the occurrence of large claims which actually cause the bankruptcy of insurance companies.The occurrence of large claims is not only interrelated but also likely to lead to the occurrence of second claims.Therefore,this paper mainly extends the risk model with delayed claims under the heavy-tailed distribution in several aspects,and obtains the asymptotic equivalence formula satisfying the corresponding ruin probability.Firstly,in the risk model with delayed claims under the heavy-tailed distribution,the distribution of the claim amount is limited to class ? which is a wider range,and the dependency structure between the claims is changed to extended negatively dependent.In addition,several factors including the random charged premium which is a nonnegative and nondecreasing random process,and the influence of interest are considered.On the basis of the tail probability estimation method and the theory of stochastic process,an asymptotical expression of the finite time ruin probability is obtained.Secondly,the bidimensional non-standard renewal risk model with delayed claims is considered.The dependent structure of the claims is expanded to the upper tail asymptotically independent.And the claim arrival is a non-standard renewal process,that is,the interarrival sequence changes from independent to widely lower orthant dependent.Besides,it is assumed that the premium income is still random and the interest force is a constant.By defining the ruin probability in two cases,corresponding asymptotic expressions are given.Finally,the absolute ruin probability in the heavy-tailed risk model with delayed claims is studied.The distribution of claim amount is extended to class ,and the influence of deductibles in actual insurance policies is considered.On the basis of the dependence of claim amount,assuming that claim amount and claim arrival interval are also dependent,and the interest factor is still taken into account,the asymptotic expression of absolute ruin probability is obtained.