The Study Of Several Models Of Proportional Reinsurance

Reinsurance is an insurance action that, in order to spread risk, control damage, andexpand its underwriting capacity; the insurer transfer all the original underwriting risk orpart of the risk to another insurer. Reinsurance helps insurance companies to avoid thecatastrophe. So reinsurance is very important for the stable operate of the insurancecompanies. Recently years, the research on the reinsurance has become a hot issue of theinsurance industry.In this paper, proportional reinsurance model with ruin probability and retentionratio are discussed. The way of reinsurance operation is simple and suitable for small andmedium sized insurance companies. Two processes, that are the insured (premiumcollection) process and the claims process, constitute the model. With different pointprocesses, three kinds of proportional reinsurance risk model were constructed.Firstly, based on the classic model of proportional reinsurance, interference andinterest rate factors were introduced in the model. The ruin probability model ofproportional reinsurance with the interference and the normal rate was constructed. Theruin probability was derived by using of stochastic processes, martingale theory, themoment generating function method. By studying the relationship between the differentreinsurance ratios different interest rates and R values, the impact of interest rates on theprobability of bankruptcy was indirectly given. Then, under the principle of the certainrisk and maximizing benefits, the optimal solution of the retention ratio was given, andthat the solution is exist and unique was proved. So some basis for decision making wasprovided to insurance companies.Secondly, based on the classic model, the premium process was expand from thelinear diversification to stochastic process. A single insurance and double insurance of theproportion re-insurance model with premiums charged by random were established. Inthis model, the upper bound on the ruin probability, the final expression for the ruinprobability and the optimal retention ratio were derived.Finally, introducing Cox process of the more generalized point process to the classic model, making the premiums collected process and the claims process closer to the actualsituation, the proportional reinsurance model under the claims process for the Coxprocess and the model in which premiums collected and claims process are both Coxprocess (ie, double-Cox) were constructed. The ruin probability under the two modelswere discussed. Also in the double-Cox model, when the two cumulative intensity areproportional, the expressions of the ruin probability and the Adjustment coefficient werederived.