Research On Risk Model When The Premium Income Is A Stochastic Process

This dissertation discusses two risk models when the numbers of premium income is a stochastic process.In condition of the continuous time model, firstly ,we discuss the renewal risk model when the numbers of premium income is a Poisson process.We get the Lundberg inequality and formula of the ruin probability by martingale method,and get survival probability in finite time period in case of exponential claims,and separately analysis the deficit at ruin and the surplus immediately before ruin by recursive method and transition probability.And then we discuss the above model with constant interest and analysis the ruin probability ,the deficit at ruin and the surplus immediately before ruin by transition probability.In condition of the discrete time model,we discuss the compound binomial risk model when premium income is a compound Poisson process,and on the basic of the model ,we also discuss the multiple line risk model by diffusion. We get the properties of surplus ,Lundberg inequality and formula of the ruin probability .