A Study Of Health Insurance Pricing Based On Multiple Loss Distributions

Health is the eternal pursuit of human beings.With the development of economy and the progress of society,people begin to pursue a better life under the condition of satisfying the basic life,and health is the foundation of enjoying a better life.In order to provide comprehensive and full-cycle health services for the people,Healthy China has been promoted as a national strategy in the Outline of the Healthy China 2030 Plan.China's basic health care system is under increasing pressure due to factors such as an aging population and changing disease spectrum.The demand for health insurance will continue to increase when the basic health care system is inadequate.In recent years,the annual growth rate of health insurance has become the first among all insurance products,and the insurance companies attach increasing importance to health insurance.In order to increase the competitiveness of health insurance products and reduce the risk of compensation,insurance companies have made a lot of efforts in the pricing design of health insurance products.At present,due to the shortage of actuarial technology and actuarial talents,there is a big technical bottleneck in determining the premium rate of health insurance.Accurate and reasonable pricing of health insurance is an important basis for insurance companies to improve product competitiveness and reduce compensation expenses,so it is necessary to study the pricing of health insurance.When the insurance company is pricing the health insurance,the core content is how to determine the loss of the insured object.Insurance companies focus on the amount paid,not the actual loss of the insured.The cost rate of insurance company,reserve fund and the problem such as reinsurance will determine with compensate pay loss,but the insurance responsibility of insurance company is the size of loss according to insurance mark will determine.Accordingly,want to be able to hold the loss distribution of insured's only,can get corresponding compensation distribution.Because the theoretical distribution has many characteristics that can help people to analyze the problem,and the theoretical distribution mostly consists of several parameters,it can reduce the work of a lot of data processing.By means of theoretical distribution,some laws of insurance liability can be inferred,and mathematical operation can also help people to get useful theoretical analysis conclusions.Therefore,this paper uses mathematical method,based on the principle of expected utility maximization,on the basis of the optimal model,using a variety of loss distribution to study the pricing of health insurance.Firstly,the paper summarizes the situation of health insurance,and introduces the development history,current situation and existing problems of health insurance.Then,based on the principle of expected utility maximization,the optimal model of the insured is established by using Lagrange multiplier method and the optimal solution is obtained.Finally,the optimal solution is numerically analyzed by log-normal distribution,gamma distribution and Pareto distribution,and the sensitivity of the key variables is analyzed.Through analysis,it is found that when the insured's loss obeys different loss distribution,different optimal amount of compensation will be obtained,and the change relationship between the key variables is also different,but the general trend is the same.