Studies On Non Totally Insurance Models Of Insurance Companies

Non totally insurance contains deductibles and reinsurance, it is an effective way of dispersing and transferring risk for insurance companies. as our country entered the Word Trade Organization, premium is determined by market and effected by international factors. So how to use Non totally insurance to dispersing and transferring risk for insurance companies is becoming more and more important. The key problem of using this method is how to choose the way of insurance and how to price it. By using mathematical models, this paper aims to give some guidance to the insurance companies for the above problems.In this paper, we use both ruin probability method and utility method to analyze Non totally insurance, from the view of ruin probability method, we try to work out and minimize the ruin probability, because ruin probability is an important criterion for measuring the stability of insurance companies. Lundberg and Cramér established the classical model, which also named L-C model. However, their model was simple and did not consider the fact of Non totally insurance. So, we use their model and analyze the effect on considering deductibles and reinsurance. and we can chose a ruin probability which insurance company can bear according to its power. Then we can price the insurance policy. By using this method, we assume that the loss fixes in with some cumulative distribution function such as exponential, Weibull, Pareto and so on. From the view of utility method, we try to maximize the utility of insurance company. By using this way, we can find out the Pareto optimal insurance policies. Artur Raviv(1976) analyzed the Pareto optimal insurance policies by using utility model, but he just considered insurance buyer and insurance company. So, using the utility model developed by Artur Raviv(1976), we try to maximize the utility of insurance company while keep the utility of insurance buyer and reinsurance company both constant. At the last of this paper, we quote F.Su&Z.Y.Yu(2002), this paper can prove some of our conclusions.There are some innovations in this paper. First, we using two methods to analyze the problem, it's more all-round than just using one method. Second, we deserve the ruin probability in some special cases while in other cases we get the characteristic of it. Third, we find that we can use ruin probability to price the Non totally insurance policies. Last, we expanded utility model of Artur Raviv(1976).