International Statistical Institute, 55th Session 2005

The Applied Research on the Loss Distribution in Reinsurance and Effects of Inflation Wang Xinjun Shandong Finance Institute Jinan(250014) China Email; [email protected]

Gao Lihao Statistics Bureau Of Chengyang District In Qingdao Qingdao (266109) China Email; [email protected]

Zhang Jun Shengli Oil Field Of Dongying In Shandong No 258 Jinan Road Of Dongying Dongying (257051) China Email; [email protected]

1.FOREWORD Calculating the insurance premium scientifically and reasonably is one of the most purpose to research property Loss Distribution. First, the amount of insured individuals is small in the property insurance, but insurance amount is enormous. If one insurance company accept it will stand considerable risk. So we must decrease the risk by reinsurance and divide loss level according to different loss amount. Insurance company locating in different loss level will charge different premium. The sum of net premium charging by each insurance company should equal to the multiplication of the rate of loss happened and Mean loss distribution function. Second, an important factor of calculating premium is effects of inflation. In order to solve this problem there are two aspects to consider: one hand as for as several common most loss distribution function considered, effects of inflation don’t affect the type of loss distribution, just some parameter change , this provides us much convenience. Another hand when thinking about effects of inflation, besides considering the change of parameter of loss distribution, we need to consider the problem of simultaneous growth of franchise. In the condition of reinsurance ,every loss level must consider the effects of inflation . We will research separately extract accurate of net premium in reinsurance and effects of inflation from several most loss distribution function as follow. 1.CALCULATING OF NET PREMIUM IN REINSURANCE We list Mean loss distribution function and Limited expected value function corresponding to several important loss distribution function by lemma. 2.CALCULATION OF THE NET INSURANCE PREMIUM UNDER EFFECTS OF INFLATION Effects of inflation have great influence on how to calculate the insurance premium. If x stands a loss variable of a certain period in the past, z stands a loss variable in now and in the future, r stands inflation rate of this period. Then, the relation between x and z can be described as follow, z = (1+ r)x . According to the relationship of the two variables, we can get International Statistical Institute, 55th Session 2005

the distribution function of the new loss variable z . Also we can prove that distribution forms of inflated loss variables for several important distribution functions such as: Pareto distribution, Lognormal distribution, Gamma distribution, Loggamma distribution, Weibull distribution, don’t change, only the parameters change correspondingly. In addition, effects of inflation also have influence on franchise(or the highest compensation amount) variable d .So when effects of inflation take place, the new franchise variable should be (1+ r)d , thus can guarantee simultaneous growth of the franchise and inflation rate. Then the calculation process of reinsurance net premium in effects of inflation can use procedures of question two.

RéSUMÉ Xinjun WANG, masculin, né en Mai 1957, professeur de l’Université de Finance de Shandong, sa direction de recherche est Contrôle par prélèvement.