Research On Risk Model With Main Claims And By-claims And Its Ruin Probability

There is a common limitation of the classic risk model and its extended models. They only take into a class of homogenous type-insurance business.But in fact,the kinds of insurance business are diversified,and the risk of operating multi-lines insurance will also increase with new kinds of insurance business empoldered and launched.So the study of the risk control in the complex situation turns into a realistic question.A new kind of risk model with main claims and by-claims was built on the basis of classic risk models in my dissertation.I made detailed investigation on this new model through the way of stochastic process and risk theory.For this type of new model,we study it mainly from these ways:First,we make further research on the nature features of their distributions;give out the probability distribution of the mixed stochastic variables,and the statistical features and the approximate distributions of the short-term individual risk models. Also the relationships between the total amount of compound compensation and individual one were investigated.At last we give out a kind of practical calculation method for the individual risk model.That is the calculation of the number of claims translating into the calculation of Vandermonde determinant.Second,a kind of risk model with main claims and by-claims is built under specific conditions.We obtain the risk process involved in this model,the statistical properties of the surplus process,and statistical features of the claim numbers and the probability distribution of the total amount of compensation.The three types of business of the risk model is given when the number of claims obey Poisson distribution and negative binomial distribution.We make a comparison between the risk model built in the thesis and the classic risk models with independent claim numbers when the amount of claims obey Weillbull distribution and Exponential distribution.The results have a good practical significance.Third,this paper makes research on the expression of ruin probability of the risk model with main claims and by-claims;obtain the specific expression of ruin probability when the amount of claims follow the Exponential distribution.At the same time,we obtain the effects on the ruin probability made by the main claims and by-claims throw the analysis of the Lundberg coefficient of the risk process.The results in this paper have important significance in business management of multi-type insurance codes and the analysis of ruin probability in the insurance actual practice.