The Research Of Environmental Liability Insurance Premium Based On The Nonparametric Kernel Density Estimation

Recently, issue of environmental pollution has become increasingly prominent. The incidence of air pollution, ocean pollution and water pollution is stepping up. To compensate those who suffered from pollution is the necessary request of civil rights. But the huge expense composed a heavy burden of the concerned enterprise and the society. To solve the problem, the environmental liability insurance system come into being in December,2007, the former state environmental protection, administration (SEAP) and the China Insurance Regulatory Commission jointly issued the Guidance on environmental pollution liability insurance work. In January2013, the department of environmental protection and the China Insurance Regulatory Commission issued Guidance about enforcement of environmental pollution liability insurance pilot work, which offered the policy basis for the environmental liability insurance.The pricing of insurance is among the most important environmental liability system content, which has three major aspects, the rating of insurance, the extraction of reserves, and the arrangement of reinsurance. The rating of insurance is the core content. The rate of the insurance directly affects the participating willingness of the enterprises and the running state of the insurance company. A scientific rate is not only favorable for the operation of the environmental liability system, but also good for the steady develop of companies and the society. Most existing studies use the parameter estimation method, which means to set the price on the basis of assumption that the claiming amount is fitting a certain kind of distribution. The non-parameter method, which use as little assumption as possible, estimate the overall distribution on the samples’distribution. After a broad research of the literature about the use of non parameter in the financial and non-life insurance field, and taking the feature of the data of claiming amount of environmental insurance, this thesis used the theory of Nonparametric density estimation in the research of rating of environmental liability insurance. The major work includes the followings.On the basis of analysis of the concept, nature and the rating features, this thesis concluded that, the procedure of insurance rating includes three steps, data reduction and the distribution fitting, the calculation of pure insurance, and the addition of the cost and the benefit. The thesis discussed the fitting method for the distribution of the data of the claiming amount, introduced the non-parameter method to the rating of environmental, and compared the two methods. After the introduction of the theory of Nonparametric density estimation and the theory of nonparametric regression estimation, the thesis focused on the Histogram method, Rosenblatt estimation method Parzen kernel density estimation and the most neighboring estimation. The thesis found Parzen kernel density estimation method has a wide range of application; theory is relatively perfect, strong applicability, so choose this method to carry on the empirical analysis. Then the thesis introduced and compared the two ways to choose window width which are in common use, based on the combination of environmental liability insurance limited data and the applicability of the method, we do empirical research on Silverman rule of thumb.With the industry of Chemical raw materials and chemical products manufacturing as the research object, the thesis set the environmental liability insurance premium on empirical research. The first was to fit the distribution of the number of claim and then estimate the probability function of the claim amount and analyze the distribution characteristic of the data of the claim. Because of its suitable conditions do not conform to the Silverman empirical law, The thesis had to transform the data; then chose the window width under Silverman rule, estimated probability density function with the application of nonparametric kernel density estimation method and inspect the result. The thesis used mathematical transform to get the function of the data of claim amount and then the expectation and the premiums.