Researches On Short-Term Health Product Pricing Based On The Surplus Process

With the improvement of medical and economic conditions, the awareness of buying health insurance products has increased over the years. Many insurance companies are continually developing various health insurance products to meet the market demand.The major topics for insurance companies are to price these products reasonably and draw ad-equate reserves.Because of the features of health insurance business, the premium pricing models are relatively simple.There are mainly three models to consider at present:simple regression analysis, aver age trend method and normal distribution method.For actual cost payment products, their claim number and claims are more random than other kinds of products, so actuaries usually need a great deal of historical data to value the risk.However. China's health insurance business is still in the early stage. Many short-term health prod-ucts are in the state of poor performance due to lack of historical data.This paper proposes a new model to deal with short-term health products. This model considers the situation that an insurance company only manages one product. We predict the future capital surplus process per policy and determine the premium by controlling the ruin probability and IRR.There are three implementation steps in this model. The first is to set initial capital and premium. Then we draw the data of claim paid per policy from the database, find out its implicit rule and estimate the loss distribution. At last, we simulate the future capital surplus process and determine the initial capital and premium. In practice, every insurance product has its own investment portfolio. In this paper, we simply choose GRACH model to fit the investment return of this product.This paper consists of three parts. The first part (Chapter one and two) introduces the pricing models used in practice and proposed in the paper. The second part (chapter 3) describes the theories of both the investment return and the distribution of loss. The last part (chapter 4) illustrates the effect of the premium and initial surplus on the probability of bankrupt by simulating future capital surplus process.There are three major contributions of this article. The first is to propose a new model for short-term health products pricing. The second is to treat the actual claim paid per month as a liner combination of the claim occurred this month and the past months. The third is to use transformed kernel estimation to estimate the claim's density function.