The Compound Binomial Model With Randomly Paying Dividends To Shareholders And Policyholders

The ruin problem is one of the significant the problems that insurance company concern. The characteristic of ruin include the time of ruin, the surplus before ruin, the deficit at ruin, probability of final ruin, and so on. The surplus of company decide whether the company is ruin or not. When the surplus is less than zero, the company is considered as bankcruptcy. So many reserchers are interested in it and make a great number of models about the surplus of insurance in acturial field. These models are called as the risk model. We can study the ruin problem through analysising the risk model. Gerber have presented the model at discrete time and discussed the probability of ruin in 1988. Those interesting result arose the climax of studying ruin problem.Among the risk models, the compound binomial risk model is classical one. It have been developed largely. The compound binomial risk model is a ideal model, but it imaginally describe the change of surplus under the conditions that the initial asset and premium at unit time are constant,and the claim change randomly. Under the risk model, it's convenient to obtian the characteristic of insurance company's ruin. The expected discount penalty function is a usual tool used to study the characteristic. So it's very important.With the development of insurance, the dividend insurance is more and more prevalent. Considering the surplus of company is no less than a certain threhold, the dividend will be paid. The researchers of risk theory build a new model based on compound binomial risk model. This paper will develop the compound binomial model with randomly paying dividends.The creative content in this paper include the following:1.Considering joint insurance company may pay dividends that include the dividend paid to policyholders and shareholders.2.Under the new model, we have obtained the recursion formation of the expected discount penalty functionΦ(u). It decides initial term.Φ(0). 3.We have obtained the formation about the characteristic of ruin.