Research On Aggregate Claim Risk Model And Ruin Probability

It should be said that from the moment of the emergence of insurance,experts and scholars consciously begin to concern the risk in insurance and control some risk of the objective world reliably. Risk is the foundation of insurance. Also, the essence of insurance is risk. And we just use the insurance to transfer our personal risks to the insurance company to minimize personal risk loss. It is worth noting that the insurance is affected by many factors, such as the initial surplus level of insurance company, the income of the insurance premium, the expenses of compensation and so on.First, this paper is based on the aggregate claims risk model,(a, b,1) class distribution and(a, b, 0) class distribution are discussed respectively. We construct the zero-Truncated Poisson distribution satisfying the(a, b,1) class distribution function. When the number of claims satisfies the zero-Truncated Poisson distribution, the differential form expression of the collective claim amount and the probability generating function of the claim number are discussed. And then we study the probability distribution of the aggregate claim amount. We also get the analysis of the aggregate claim amount of the moment expressions. The paper also gives numerical simulation of the relationship between the moment of the claim amount and the number of claims in the numerical simulation. With the increase of the number of claims, the mean and variance of the collective claim amount will be increased. When the individual claim is continuous, it is found that the smaller the mean value of the continuous distribution is, the higher the fitting degree of the discretization method is.Secondly, the innovation definition of the discrete time of the loss of ruin probability is defined for the initial surplus u, the amount of loss is not greater than y. The influence of different parameters on the probability of loss of ruin probability under the condition of numerical simulation are given. Data show that when the loss boundary is fixed, with the increase of the level of the initial surplus, the probability of the loss is gradually reduced. When the initial surplus level is fixed, with the increase of the loss boundary, the probability of the loss of the bankrupt probability increases gradually.