Ruin Probability In The Risk Model With The Limit Of Ruin In Variation

The classical risk model and the generalized risk model are studied in many papers, andgive some useful conclusions. But most of the papers assume that the limit of ruin ofinsurance companies is zero, actually in insurance business, when the insurance company’searnings fall below a certain level (the ruin limit), the insurance company need to adjustpolicy or declared bankrupt. At the same time, considering the insurance company profits, theinsurance company’s earnings must be above the level of some positive number, and alsoshould be a function of time (variable ruin limit). In non-life insurance, when the risk ofinsurance liability is homogeneous, the policy-holder from the distribution of the number ofclaim must have a general hypothesis for the Poisson distribution. If the risk of insuranceliability is non-homogeneous, the policy-holder from the distribution of the number of claimmust have a general hypothesis for the negative binomial distribution.This paper considers the actual situation, divides into four chapters to discuss.The third chapter assumes premium arrival is Poisson process, the occurrence ofrefunding and the arrival of the claims which are normal or abnormal is thinning process ofthe arrival process respectively, and get the corresponding Lundberg inequality.In the fourth chapter which based on the third chapter considering the arrival process andclaims obedience to negative binomial distribution, and get the corresponding inequality ofthe ruin probability and Lundberg inequality.The fifth chapter focuses on the initial capital and premium are subject to interest rateand investment rate of return, And get the corresponding inequality of the ruin probability andLundberg inequality at last.In the sixth chapter, considering random disturbance in the three models, the study in thispaper can better approximate to the actual situation.