Application Of Graduation In Estimating The Incidence Of Critical Illness

The critical illness insurance conforms to the trend of regulator and satisfy the needs of the people with an increasing living standard,plays an increasingly important role in the insurance market.The incidence of critical illness directly affects the rate of the product,and it also provides reference information about hwo to develop and design products for insurance companies.Therefore,the empirical evaluation of the incidence of critical illness used by insurance companies is a very critical part of product design.Graduation is a method of correcting estimates based on the preliminaryly estimated by the observation data.It is widely used in various fields,especially in the actuarial work of life insurance.All mortality or morbidity tables must be rounded off from empirical data to make the results more reliable.This paper finds that the development of graduation in the application of morbidity lags behind its development in mortality.According to the characteristics of the incidence of critical illness,this paper introduces the discrete Beta kernel function graduation(fixed bandwidth and adaptive bandwidth)used in mortality graduation,malignant tumor are selected as representative of critical illness,and compare the graduation effect on the incidence of malignant tumor of the two kinds bandwidths of discrete Beta kernel function graduation with the three traditional graduation methods(moving weighted average graduation,Whittaker graduation and spline graduation)commonly used in incidence of critical illness.The results show that:the moving weighted average graduation adjustment parameters are more severely restricted and there are end-value problems;Whittaker graduation can get good smoothness and fitness indexes but has a large amount of calculation and has limited effects on local fluctuations and extreme values;Spline graduation has a better effect on local fluctuations and extreme values,but it depends on sufficient and reliable prior information and the amount of calculation increases with the number of nodes.The calculation of the two kinds bandwidths of discrete Beta kernel function graduation is relatively simple.While ensuring the smoothness index and the fitting index,its effect of processing local fluctuations and extreme values is also ideal,the adjustment space for parameter under adaptive bandwidth is more flexible and theoretically can more accurately assign the weight of the rude value sequence.Finally,based on the results of the comparation analysis and the development status of critical illness insurance,this paper intends to make reference recommendations to the insurance company on the estimation of critical illness incidence to promote the development of critical illness insurance products.