Study Of The Joint Distribution Of The Time Of Ruin, The Surplus Immediately Before Ruin And The Deficit At Ruin In A Risk Model

In this paper, the joint distribution of the time of ruin, the surplus immediately before ruin and the deficit at ruin in a risk model with stochastic premium and constant interest force are studied. The classic Cramer-Lundberg model simplify the premium process to a linear function of time and take no account of interest.Considering the insurance practice, we will create a risk model that not only assume premium process as a stochastic process but also take account of interest. In the first chapter, we introduce the development of the known risk models and how we create the new model upon them in this paper. Then, we illuminate the structure and assumption of the new risk model. In chapter two, the deduction of the distribution of "Earning-Paying" at time t and the proof of two basic theorem are carried. On the previous work of the first two chapters, we derive the explicit expression for joint distribution of the time of ruin, the surplus immediately before ruin and the deficit at ruin and some other propositions during the fourth chapter. At the last chapter, we will derive the upper bound of the ruin probability and make a concrete example.