Research On Loss And Claim Distribution Fitting Methods In Non-life Insurance

In non-life insurance, the premium valuation, loss and claim of insurance are the core issue, and to consider the premium pricing must first know the loss distribution. Therefore, the loss of distribution fitting methods research is very important. In the thesis, first, it is studied the traditional methods of loss of distribution fitting, that the initial identification of distribution, the estimation of parameter and the test of fitting degree, from theoretical and practical aspects, and then introduced the fitting methods on the basis of the orthogonal polynomial. It is used the fitting methods based on orthogonal polynomial to study a practical problem, and achieved better results, that provide a new method for the loss of distribution fitting.In the thesis, the main conclusions are below: based on the value of approaching theory, introduced a new method described loss distribution -- the loss distribution fitting methods based on orthogonal polynomial, the method directly from the sample information and orthogonal polynomial to fit, not assume a classical probability distribution first, thus mathematics and insurance practical meaning are more significance. Using orthogonal polynomial and eventually into the general polynomial to fit the loss of distribution, it can avoid the complexity and instability of simultaneous equations calculation, and based on data analysis to determine the frequency value of polynomial named m without subjective experience restrictions, in the calculation it may get the fit polynomial coefficients in order, avoid complex numerical value calculation. In addition, the orthogonal polynomials are orthogonal each other, when adding or reducing (maximum) items, the coefficients of lower items do not change, which avoided double counting. The final loss distribution model can be used for the fitting of insurance loss.The results of this thesis are further enriched and developed the theory and method of the loss distribution fitting of non-life insurance.