The Ruin Probability For Negative Risk Model With The Compound Poisson Process

Ruin theory is the core of risk theory. The studying of ruin probability and itspractical applications has the important significance. Along with the development of risktheory to mature and widespread, the traditional classical risk model is already far can'tsatisfy today's demand, thus a multi-angle promotion would be more close to the actualsituation.In this paper, we considered the content which is promoted from traditional classicalrisk model and its generalized negative risk model. Considering the practice, we firststudied the negative risk model with the compound Poisson process, whose claims ofmulti-type insurances happened at the same time. This model is generalized from one withsingle type of insurance. In this model, insurers' premium income is a negative constant,the m-fold insurance has claims at the same time, and claims models are compoundPoisson process.Second, we considered the negative risk model which extended by considering adependent structure. The situation is that the arrival of claims is a p-thinning process of thearrival process. Insurance policies were the basic of this model. In this model, insurers'premium income is a sequence of random variables. Claims process is a compoundPoisson process.Third, we researched the negative risk model which extended by considering adependent structure. Insurance compensations were the basic of this model. In this model,insurers' premium income is a negative constant. Claims process is compound Poissonprocess, and a kind of death benefit is produced with probability p.In this paper, The equation on adjustment coefficient is given. We researched andsummarized the ruin probability and application of the negative risk model by themartingale method. Furthermore, the Lundberg inequality is derived. And then, the limit ofruin probability is given.