Three Types Of Classical Risk Model To Promote Research

The risk theory is the basic discipline of learning financial mathematics and the actuarial mathematics of insurance and its core is the study of the ruin theory. In this text, based on the classical risk model ,we construct and research three kinds of new risk models . Finally we obtain some expressions or characters of the variables about ruin.Five chapters constitute this text.In the first chapter, we introduce the history, the present conditions of the risk theory and the main results, and we especially pay more attention on the classical risk model, finally we present the main content of this text and the main results of my research.In the second chapter, we outline the knowledge about expectation, Laplace transform, point process, martingale etc. We also outline some useful theorems. This knowledge is also the foundation of the text.In the third chapter, we firstly extend the classical risk model, and then we construct a new double-multiple risk model. This model contain both positive and negative risk sums. The common negative risk sums process is life annuity insurance. A big life insurance company has life annuity insurance and personal accident insurance also. Then we analyze and discuss this model, and we get the integral-differential equation for the survial probability under different conditions, finally we get the Lundberg inequality for the ruin probability.In the forth chapter, we firstly point out the limitation of the classical risk model, that is the premium rate c is a costant, but actually, the number of reaching insurance bills in the different units of time is often not the same, it is a random variable, and the premium of different insurance bills is also a random variable. We studied a special case of this type of model, that is, the process of collecting insurance premium and process of claims are Poisson process, as well as both the premium of each insurance bill and the amount of each claim are exponentially distribution. we get the Lundberg inequality for the ruin probability and the upper bound estimation of the ruin probability before time t.In the fifth chapter, we firstly point out another location of the classical risk model, that is the classical risk model didn't consider the influence of the interest rate, but actually the interest rate is a important factor. We construct a new risk model under the constant interest, as well as the number of both collecting primium and claiming are binomial distribution, and the premium of each insurance bill is random. Then we analyze and discuss this model, finally we get the Lundberg inequality by using martingale method.