Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer
Peng Yang and
Zhiping Chen ()
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Peng Yang: School of Mathematics, Xi’an University of Finance and Economics, Xi’an 710100, China
Zhiping Chen: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
Mathematics, 2023, vol. 11, issue 10, 1-28
This paper investigates the optimal private health insurance contract design problem, considering the joint interests of a policyholder and an insurer. Both the policyholder and the insurer jointly determine the premium of private health insurance. In order to better reflect reality, the illness expenditure is modelled by an extended compound Poisson process depending on health status. Under the mean–variance criterion and by applying dynamic programming, control theory, and leader–follower game techniques, analytically time-consistent private health insurance strategies are derived, optimal private health insurance contracts are designed, and their implications toward insurance are analysed. Finally, we perform numerical experiments assuming that the policyholder and the insurer calculate their wealth every year and they deposit their disposable income into the Bank of China with the interest rate being r = 0.021 . The values of other model parameters are set by referring to the data in the related literature. We find that the worse the policyholder’s health, the higher the premium that they pay for private health insurance, and buying private health insurance can effectively reduce the policyholder’s economic losses caused by illnesses.
Keywords: illness expenditure; leader–follower game; premium; private health insurance; stochastic optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:10:p:2240-:d:1143934
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