By using a total sample of 31,074 observations from April 2009 to December 2013, this study tries to explore the adverse selection or the moral hazard problems due to information asymmetry for a life insurance company. To test whether the presence of asymmetric information problems, this study establishes a linear regression model to analyze the relationship between the insured amount and the time of initial claims or claim payments. The control variables include insured age, gender, premium frequency, and region. The empirical results show that the insured amount, the insured age, gender, premium frequency, and region are significantly related to the time of initial claim or claim payment. Thus, it is reasonable to suspect that the asymmetric information problems of permanent Medicare Health Insurance do exist.