Optimal time‐consistent social health insurance and private health insurance strategy under a new health insurance framework

Abstract

A new continuous‐time health insurance framework is proposed to simultaneously determine the optimal social health insurance strategy and optimal private health insurance strategy. The social health insurance can cover both the expenditures of general illnesses and critical illnesses, while the private health insurance only covers the expenditure of critical illnesses. To reflect the inevitable connection between critical illnesses and general illnesses, we assume that the number of critical illnesses and the number of general illnesses are positively correlated. The policyholder's objective is to find an optimal time‐consistent social health insurance and private health insurance strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. Explicit solutions for the optimal time‐consistent health insurance strategy and the corresponding value function are obtained by employing the stochastic control technique. Finally, we numerically examine the influence of expenditure parameters on the optimal time‐consistent health insurance strategy, and also examine the effect of the health insurance on the policyholder. The results reveal the similarities and differences between social health insurance and private health insurance, which provide insightful guidance for health insurance practice in reality.

A firm-level analysis of Chinese commercial health insurance surrender

“…Method 2, method of deleting explanatory variables, that is, deleting the value and appreciation rate of capital (CRNA) in explanatory variables of the model. Another set of estimated results is shown in column (3). By comparing columns ( 1) and (3) in Table 7, it can be found that, compared with the regression of "PW+PCSE…”

“…(2) In terms of the individual variables, divorce, non-urban residential areas, apartment type of housing, non-ownership of homes, and bad relationship with siblings increased the surrender rate. (3) In terms of the financial variables, low income, low expenditure, the existence of children that incurred child care expenditure, not expecting to bequest from spouse, not holding public health insurance, and expecting to benefit from a retirement pension increased the surrender rate.…”

“…Since the reform and opening-up for more than 40 years, China's commercial health insurance industry develops rapidly [1][2][3][4][5], at the same time, the surrender amount of the commercial health insurance industry is also high, and the surrender problem is relatively serious [6,7]. In 2019 and 2020, for example, the surrender amount of several professional health insurance companies increased: the surrender amount of "Ping An Health" was CNY 2.0321 million and CNY 3.1678 million respectively, with a year-on-year growth of 55.89%.…”

Study on the Dynamic Relationship between Chinese Residents’ Individual Characteristics and Commercial Health Insurance Demand

“…Since the commercial health insurance industry of China resumed operation in 1982, its business scale has become increasingly large and its development speed has advanced rapidly [ 2 , 3 , 4 ]. In terms of the number of companies, this increased from 1 in 1982 to 164 in 2020; in terms of premium scale, this increased from CNY 57.4 billion in 2009 to CNY 817.3 billion in 2020, and the annual compound growth rate reached 24.78%, higher than the life insurance premium income of 10.22% and accident insurance premium income of 14.55% in the same period.…”

Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer

“…It may be very difficult to choose an appropriate stochastic process to predict dynamic illness expenditure. The Poisson process may be a good choice; recently, [22] adopted the Poisson process to describe the number of illnesses, and used the compound Poisson process to describe the cumulative expenditures of illnesses. Nevertheless, this method cannot reflect the influence of health status on illness expenditure.…”