Research On The Discrete Risk Model Under Two By-claims With Constant Dividend Strategy

In insurance theory, the risk model has been a very important part. With research continues to deepen, the classic model from simple compound poisson risk model gradually deepening to a variety of complex risk models, research content from a single ruin probability calculation, Gerber-Shiu discount penalty function ruin feature quantity, etc., to gradually extend to consider the introduction of a number of risk models with strategies, such as dividends, investments, reinsurance strategy, etc. But, the demand for more diverse insurance products on the market comes to produce the cases of multiple by-claims gradually. For example a flood catastrophe floods the insured’s home, then insurance companies not only need to pay property insurance of housing, vehicles, etc., but also the insurance company may pay personal insurance if the insured hurts his body during the flood catastrophe; if the insured infects with the plague caused by the disaster lead to serious illness or death, then the insurance company may also need to pay medical insurance or other insurance. This condition can consider the two followed payments as two by-claims of the flood insurance, the two by-claims are independent of each other and may occur at the same time. However, previous studies mainly focused on the research of a single claim, studies on by-claims are few, there is little literature on the study of multiple by-claims. Therefore, the study on cumulative dividends of insurance company under multiple by-claims and by-claims maybe delayed, not only it can promote the development of the insurance practice, but also it can improve the risk model theory research, it has a strong practical value and theoretical significance.Firstly, this paper studies the theory related. Secondly, based on constant dividends strategy, under the discrete frame and two by-claims which are mutual exclusive, we study the cumulative dividends before the ruin and carry out a case study. Thirdly, based on constant dividends strategy, under the discrete frame and two by-claims which are independent, we study the cumulative dividends before the ruin and carry out a case study. At last, we compare the results of the both.Through this study, we get the following conclusions:When other conditions remain unchanged, the cumulative dividends increase with the initial surplus increases, the cumulative dividends increase with the occurrence probability of by-claims increases, the cumulative dividends decrease with the dividends barrier increases, the cumulative dividends of the two by-claims which are mutual exclusive are more than the two by-claims which are mutual independent. Through the analysis, insurance companies should raise the initial reserve ratio appropriately, prepare adequate risk fund, reduce the risk of payment; increase the proportion of by-claims of insurance products appropriately; reduce the threshold dividends appropriately; increase the proportion of the insurance products which main claim only cause a by-claim every time during underwriting two by-claims insurance products. These suggestions are set to increase the cumulative dividends of the insurance company and to attract investors.