Ruin Probalities In A Risk Model With Stochastic Premium Process

In this paper, ruin problems for an insurance company are studied. In the classic Cramer-Lundberg model, the premium process is a linear function of time. In this paper, besides the invariable premium income rate, the risk models are allowed to exist another stochastic premium process. Thus, the new premium income process is given as the sum of a linear function of time and a compound Poisson process. An integro-differential equation satisfied by the survival probability is obtained. By martingale method, upper bound for the ultimate ruin probability is given. When the the premium and the claim amount follow exponential distribution or Erlang(2) distribution, some disirable results on the ruin probability are presented. When the surplus is invested in the market,An integro-differential equation satisfied by the survival probability is obtained. Especialy,by classic differential equation method,an approximate estimate of the survival probability is given ,when the premium and the claim amount are both distributed as exponential.