The modes of piecewise and the number of intervalsare particularly important in the formulation of compensation scheme for critical illness insurance in China. In this paper, under the three subsection modes of interval bisection, constant ratio increment and constant ratio decrement, the theoretical models are established with interval quantity as independent variable and serious illness insurance compensation amount as dependent variable. Taking the expected compensation ratio as the standard to measure the compensation level of serious illness insurance, we can get the following results: first, the optimal number of
intervals corresponding to the three interval modes are respectively: 3, 3 and 5; second, under the setting of the number of piecewise, the compensation level of the interval equal proportion increasing mode is the highest, the interval equal proportion decreasing mode is the second, and the compensation level of the interval equal proportion increasing mode is the lowest, But there is little difference between the three. Then, based on the data of CHARLS in 2015, we calculated the incidence of family catastrophic medical expenditure under the three interval modes as 7.13%, 7.26% and 7.69% respectively. The result is consistent with that of the theory.
QIU Chunjuan,GAO Shuhui,QIAN Linyi. Study on the Number and Mode of Optimal Piecewise of Critical Illness Insurance in China[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2022, 38(1): 138-150.