Research On Actuarial Model Of Medical Mutual Aid Guarantee Based On Risk Loss Distribution

As recently as the end of “The 12 th five-year plan”, the contradiction between the reality of the “low lever and broad coverage” of our medical insurance system reform and the demand of fully achieving the goals of health care reform and constructing a basic health care system turns to be increasingly conspicuous, which requires us not only to consolidate the social security system, which is made up of the basic medical insurance and commercial insurance, but also to do further research on the rising mutual medical insurance towards workers, which complements it. Although the mutual insurance is able to develop under the guidance of government policies, from the existing researches, the Premium calculation in our country often take use of roughly estimation method and study usually focuses on the theories. Meanwhile, little research has been done in the area of insurance product design, which increases the operating risks of mutual medical insurance towards workers and constrains sustainable development. Using the mature risk theory from the realms of commercial insurance for reference, we learn that the core issues of the mutual medical insurance include product design, set-up reserve, and solvency management. Furthermore, the fundamental impact of these problems is the riskiness of the target, namely, claim sizes distributions.Based on the actual loss data from the mutual medical insurance towards Yunnan province workers, this article combines the parametric estimation and the non-parametric estimation to explore premium actuarial models to fit the data better and to provide thought for the investigation of the loss distribution and the premium calculation according to the characteristics of data. First of all, this paper takes a brief review of the status of domestic and foreign research on medical insurance to look for available actuarial method for mutual medical insurance. Secondly, on the basis of analyzing the actuarial method which has been mainly used in medical insurance, we propose a premium calculation method based on loss distribution. Then, we describe some related theories on risk loss distribution, non-parametric estimation and so on. In the end, under the tendency that workers get subsidies in sections at present, the actual loss data are disaggregated by age and by gender before we adopt the data mining notion to build premium calculation models according to the characteristics of data.The result indicates that the characteristics of the loss data are still shown as heavy-tailed distributions, that is to say, negatively skewed distributions, after partitioning. For one thing, in the groups who have passed the fitness test, burr distribution of three-parameter and log gamma distribution give better fitting in comparison with the two-parameter heavy-tailed distributions which are widely used. While non-parametric kernel density estimation widely perform better than parametric estimation. For another, if the assumption that data comes from the same distribution fails, the conventional heavy-tailed distribution may not fit the loss data well. In this circumstance, we group the data by threshold based on the extreme value theory to build superposition model of the claim sizes distribution, which combines the parametric estimation with non-parametric estimation. In the end, we take the net premium calculation as an example to introduce the analytical method of the superposition model.