Risk Model With Random Premium Rate And Risk Model With Two Compound Poisson Processes

In this paper, we study the risk model with random premium rate and the risk model with two compound Poisson processes. Then we get ruin probability, actuarial diagnostics and Lundberg inequality in the new model.As to the risk model with random premium rate, we concerned with discrete random variable, continuous random variable and general random variable. We derive the formula of ruin probability, the extreme during the total duration of negative surplus and the joint distribution of the surplus immediately before ruin and the deficit at ruin.About the risk model with two compound Poisson processes, we discuss the risk model with two compound Poisson processes and the risk model with two compound Poisson processes by diffusion. Then we get Lundberg inequality and the formula of ruin probability in this new model.