Discrete Multi-type Model And Its Application

Risk theory is popular topic in the present actuarial science and mathematics science. It helps to construct the risk model in the light of the instrument of stochastic processes and to study the problems of ruin probability and adjustment coefficient. The scale of the business expands incessantly and the types of insurance increase. Considering the limitations of the classical risk model and other generalized risk models, the multi-insurance risk model has been constructed.This thesis mainly deals with two-type risk model, three discrete risk models has been constructed. In chapter 1 we briefly reviewed the risk theory and its development. The significance about this paper is expressed. In chapter 2 we define the fully discrete multi-type risk model and the model is explored systematically. Particularly, discuss several random variables to the time of ruin. the probability of ultimate ruin, the distribution law of the surplus immediately before ruin and the deficit at ruin are discussed with emphasis. On this foundation, we make some expansion in chapter 3 and chapter 4,the general formula of ruin probability for this model is given and Lundberg inequality is got. In chapter 5 we briefly review the whole paper and put forward the further tasks.