The Study Of Several Kinds Of Risk Models

With insurance practices increasingly influenced by other factors in recent years,the classical single risk model obviously cannot meet the demand of the reality,so consider including the distribution of the multiple factors mixed risk model become a new trend.Traditional classical risk model is divided into the positive risk model and the negative risk model.In this thesis,based on positive and negative risk model corresponding with several risk model with random premium and interference,study on the bankruptcy related properties of the models.The main research contents are as follows:1.On the basis of the classical compound binomial risk model,which proposes the compound binomial with stochastic binomial premium bivariate discrete model.Get the Gerber-shiu discounted penalty function to meet the defective renewal equation and analytical solution, the recurrence formula, the asymptotic solution and its integral equation,the formula of ultimate ruin probability, the asymptotic solution and integral equation, the surplus and deficit distribution function of bankruptcy before the bankruptcy of recurrence formula and the asymptotic solution.2.Study on multiple insurance risk model with interference, the stochastic process theory and risk theory gives the related properties of the ultimate ruin probability、the finite time ruin probability and the distribution of the bankruptcy moment,and the model example analysis is given.3.Firstly discuss on contains positive and negative risk model of risk management process by disturbed,get the related properties and bankruptcy related of risk model with stochastic premium;model bankruptcy moment conditions are obtained by martingale method expectations explicit and model for finite time ruin probability is given and the distribution of the bankruptcy moment recurrence formula;Before the deficit distribution and the resulting model has failed in instantaneous surplus distribution and joint distribution.