Research On The Ruin Probability Of Two Kinds Of Risk Models Related To Poisson-Geometric Process

In the insurance and related industries,due to the complexity of the external financial environment,the company's operation is faced with certain risks,and even the possibility of bankruptcy.Therefore,ruin probability has a very important practical significance for the company,which has aroused extensive attention of scholars and experts.In this paper,we study the ruin probability of two risk models related to insurance companies.The first model is a one-dimensional risk model,in which the premium includes two parts: linear growth and compound Poisson process,and the claim is compound Poisson-Geometric process.The second model considers a two-dimensional risk model with perturbation,in which the counting process of premium and claim is Poisson-Geometric process.The properties of Poisson-Geometric process in practical application are better than traditional Poisson process,and it is a kind of extension of Poisson process [4].Therefore,Poisson-Geometric process is used in the counting process of both models in this paper.We study the ruin probability of the first risk model from the point of view of equation and get the differential and integral equation of the infinite time survival probability and the partial differential and integral equation of the finite time survival probability respectively.Under the exponential distribution of premium and claim,the above differential and integral equation and partial differential and integral equation can be reduced to ordinary differential equation and partial differential equation respectively,and the exact solution of ordinary differential equation can be obtained.For the second risk model,using the theory of martingale and stopping time,first get the upper bound of the ruin probability;the second considering the premiums and claims vector interior has FGM dependency structure,get the change trend about the upper bound of the ruin probability with the related parameters,the corresponding intuitive explanation in economics is also given;the previous section assumes that premiums and claims follow a light-tailed distribution,in the last part,we study the asymptotic expression of the ruin probability of the risk model when the claims follow the heavy-tailed distribution and the initial fund vector tends to infinity.