With Interference Multi-risk Model With The Joint Distribution And Reinsurance

Risk theory is a important branch of modern mathematics, which ismainly applied in finance, insurance, securities investment and the riskmanagement. Nowadays, the collective risk theory is one of the mostintriguing fields both in actuarial and mathematical science. There aremany researches on one-type risk model. It is necessary to buildmulti-type risk model for extending of managing scales. This thesismainly study multi-type risk model with random disturbing item.Firstly, it is summarized the classical risk model and itsgeneralizations and reinsurance. Secondly, The model of literature [42]that the processes of premium income and claims arriving are Poissonprocesses is generalized to what the processes of premium income andclaims arriving are generalized Poisson processes. The top and the bottombound of the adjust coefficient are obtained. Thirdly, The model ofliterature [54] is generalized to a multi-type risk model, the expression forthe joint density function of three characteristics: the time of ruin, thesurplus immediately before ruin, and the deficit at ruin is deduced. Byusing the joint density function, some Dickson's results is generalized tothe multi-type risk model and the distribution of the time that the negativesurplus first reaches the level zero is also obtained. At last, a multi-typerisk model with random disturbing item is constructed. The boundary of adjust coefficient R is discussed under proportional insurance andexcess insurance respectively. It is gained the equations of adjustcoefficient R and coefficient of proportional insuranceα, equations ofadjust coefficient e and coefficient of excess insurance M when clamsobey exponential distribution. The values of parameters are given tomake simulation. The changing trend of R according toα, andchanging trend of R according to M are obtained which is the same asthe result of reinsurance of classical risk model.