The phenomenon of adverse selection caused by asymmetric information dominates the insurance market. In this paper, based on principal‐agent theory, we establish a two‐period dynamic insurance contract model with a low compensation period. This model introduces the tools of a low compensation period and the increase and decrease in the bonus to identify the risk types of policyholders. We prove that this model can achieve a strict Pareto improvement relative to the two‐period static insurance contract model with a low compensation period. Moreover, we also graphically analyze the conclusion, which can help insurance companies to design more comprehensive insurance contracts.

In the case of incomplete environmental liability insurance, enterprises are likely to go bankrupt. Rational enterprises generally do not want to insure the environmental loss liability in case of bankruptcy even if they are compensated by insurance companies. This means that the premium calculated now is high, which may be the main reason for the current enterprises to cherish insurance. Based on this, a basic model of environmental liability insurance contract considering bankruptcy under ex ante asymmetric information is established. The model is improved by using the information screening combination tool, which further improves the efficiency of information screening.