Abstract: In the markets of insurance, there extensively exists information asymmetry which causes the phenomenon of adverse selection, in order to avoid this phenomenon more effectively that influences the efficiency of insurance market, the two-stage insurance contract models with bounties and penalties were established according to the two and multiple risk types of insureds in this paper, which shows that bounties and penalties can be used to distinguish the risk types of policyholders for the first time. These models indicate that in the second period of insurance the insurers can give the insured bounties or penalties in terms of the claim or not by policyholders in the first period, the probability of obtaining penalties is far more greater than bounties in the second period if the insureds of high-risk choose the insurance contract designed for the low-risk, namely the high-risk policyholders are more afraid of penalties and thus the model meets Spence-Morris separation condition. This insurance contract model with expected profits of insurers still being zero, which does not lead to extra economic burden for insureds, can yet realize the strict Pareto improvement compare to the two-time repeat model of traditional partial insurance contract. Furthermore, the insurance contract model with bounties and penalties proves that as long as the insureds with each different risk type are incentive compatible to the policyholders of the highest risk type, they are incentive compatible to every risk type of insureds, which greatly simplifies the two-period insurance contract model under the conditions of various risk types. An example is given to illustrate the effectiveness of the model at last. In addition, our study not only presents a new screening tool, but also make a major step forward in the research of Multi-period dynamic insurance contract.

Key words: asymmetric information, adverse selection, two-stage insurance contract, bounties and penalties, Pareto improvement