The Issues Of Compound Binomial Model Under Random Environment Are Researched

With the rapidly development of insurance industry and gradually change of business environment,the classical risk model has been unable to depict the risk of reality of insurance company,so the risk model in random environment get increasing attention of scholars.Risk theory research not only provided measure methods for management risk of insurance company,but also provided important theory basis for steady business.In reality,the surplus of insurance is mainly affected by interest rate,premiums,claims and dividend.In market,the insurance company pursuits profit maximization and risk minimization at the same time.Company cannot be ignored the interest that comes from company's surplus invest bank or free risk products.Owe to the existence of competition,insurance company may lost or obtain customers,meanwhile in order to enhance the interest of customers,premium may be random,thus them depicted by random variables are more appropriate.In order to attract investment,dividend is often adopted by company to shareholders,namely insurance company will pay a certain amount dividends to shareholders when surplus meet the given conditions.This paper researched the risk model of discrete time,consider the compound binomial model with interest rate of homogeneous Markov chain,the number of premium is binomial process and random premium amounts.We analyses the properties of surplus process,deduced the equations of ruin probability,and obtained Lundberg inequality by inductive approaches.Further,for the type insurance products with dividend,we assumes that the amounts of dividend is a random sequence of take bound value,and premium rate is a function of adjustment with surplus,study compound binomial model with dividends under stochastic interest and random premium.The equation of ruin probability and the expression of joint distribution of ruin time,the surplus before ruin and the deficit at ruin have been deduced.Then we illustrated the impactions of premium and dividends to ruin probability by a numerical example.