Studies Of Several Reinsurance Risk Model

This subject is based on the classical compound Poisson risk model to researchproportional reinsurance and excess of loss reinsurance risk model. On the basis of actualrequirement, promoting the compound Poisson process, number of premium collectionprocess for negative binomial random process and number of claim process forPoisson-Geometric random process is discussed.Firstly, the related theory knowledge is introduced, such as risk model, ruinprobability, accommodation coefficient, Martingale method negative binomial distributionPoisson-Geometric distribution and Cox distribution.Secondly, this paper discusses compound Poisson reinsurance risk model. Firstly, arisk model with proportional reinsurance considers rate of interest, inflation rate and thelimit of ruin. Ruin probability is given. The more proportionality coefficient ofreinsurance, the more accommodation coefficient, the smaller ruin probability is. Secondly,this paper discusses compound Poisson excess of loss reinsurance risk model, obtainingthe upper and lower bounds of the accommodation coefficient. Lastly, this paper considersCox process reinsurance risk model, showing the expression of ruin probability. When thelimit of insurance company claim is increasing, the smaller accommodation coefficient, ruinprobability is more.Thirdly, this paper discusses a reinsurance risk model that number of premiumcollection process is negative binomial random process. Firstly, negative binomial randomprocess proportional reinsurance risk model is discussed, showing the expression of ruinprobability. Secondly, this paper discusses risk model that main claim may produce aby-claim which may be delayed, showing the expression of ruin probability. Lastly, thispaper considers negative binomial random process excess of loss reinsurance risk modelwith random disturbance term. When the claim is exponential distribution, the relationbetween accommodation coefficient and the limit of insurance company claim is obtained.Lastly, this paper discusses compound Poisson-Geometric reinsurance risk model.Firstly, this paper discusses compound Poisson-Geometric proportional reinsurance riskmodel with surrender. The number of premium collection process is negative binomial random process. The number of claim process is Poisson-Geometric process. Thesurrender is compound binomial. The ruin probability is obtained. Lastly, this paperdiscusses compound Poisson-Geometric excess of loss reinsurance risk model, obtainingthe relation between accommodation coefficient and the limit of insurance company claim.