Ruin Probability Of A New Dependent Risk Model With Stochastic Premiums

In today's rapid economic development,people's risk awareness and the sta-tus of insurance industry is gradually increasing.For insurance industry,it is very important to identify and manage risks and strengthen the study of risk theory.Ruin theory is the core content of risk theory.A full study of it can help in-surance companies develop appropriate business strategies and improve economic efficiency.With the development and maturity of bankruptcy theory,the classical risk model can no longer reflect the actual situation,so it is necessary to improve the model to meet the practical needs.This thesis starts from stochastic premium dependent risk model,because the dependent relationship of the model is based on a policy only causes one claim with a certain probability,it is not applicable to some insurance products.Based on the double compound Poisson risk model,this thesis considers a policy can cause multiple claims,by using negative Binomial thinning operator to describe the situation that the policy causes n claims with the probability of p(1-p)ⁿ.A new dependent risk model with stochastic premiums is proposed.The Lundberg upper bound of ruin probability of the new risk model is obtained by martingale method,and the influence of initial reserve,premium,claim and the value of thinning operator p on ruin probability is analyzed by numerical simulation.Moreover,we consider the market fluctuations,the Lundberg upper bound for ruin probability of a perturbed risk model is obtained,and the influence of the diffusion coeffcient?on ruin probability is analyzed by numerical simulation.