The Ruin Study Of A Risk Model With A Random Premium

In this paper, on the substructure of the classical risk model ,This thesis mainly changs the consant premium income of the classical risk model into the random premium income of the risk model ,so that it is much fitter for the practical operation of insurance company. Firstly ,creating three risk models: a discrete time risk model with a random premium , the two compound biomial risk models, a risk model with a investment when the number of premium income is a possion process, secendly , we obtain several important ruin probabilities and distributions in the risk theory: the ruin probability in finite time , the ultimate ruin probability, the distribution of the ruin time ,the distribution of surpus immediately before ruin and the deficit at ruin .In chaper 1. To introduce the situation of insurance in our country at present ,the significanc of this thesis and the classic methodsIn chaper 2. under the discrete time, I create the risk model which its premium and claim are random variale and prove that the surplus Un at n time is a markov chain with transition probability, we obtain several important probabilities and distributions in the risk theory: the ruin probability in finite time ,the ultimate ruin probability, the distribution of the ruin time ,the distribution of surpus immediately before ruin and the deficit at ruin . The Lundberg unequality is obtained by the discrete martingale approach .In chaper 3 .Under the discrete time ,we disguss a new model which both the arrival of premium policies and the occurrence of claims follow two compound Binomial processes . we obtain the series expressions of several important probabilities in the risk theory: the ruin probability in finite time ,the ultimate probability,the distribution of the ruin time, the distributions of surpus immediately before ruin and the deficit at ruin . And we prove the integral equations of ultimate ruin probability .As an application , we give the method of ruin probability for the case of exponential distribution. The Lundberg unequality is obtained by the discrete martingale approachIn chaper 4 .under the continual time ,we creat a risk model perturbed by diffusion,which its premium process is a possion process and its claim process is a compound prossion process. we obtain it's probability of riun and Lundberg's inequality by a martingale method...