Insurance Contract Design of Deductible and Claim Times under Moral Hazard

The insurance contract based on Bonus-malus System design is widely used in real life. If the insured had less claim numbers in the previous stage,he would be reduced the premium and the compensation won't be affected by its inverse impact. Which can motivate the policy-holders to avoid accidents. Combining deductibles and claim numbers in the design of single-period insurance contract and changing deductible of each accident along with the increase of the claims numbers will maximize policy-holder's utility. Note that when the moral hazard is not considered and in order to make the insured being able to obtain the highest utility, the value of deductible in the insurance contract should decrease accordingly along with increase in the number of claims. On the contrary, when the moral hazard is not considered, it will increase accordingly with the increase of the number of claims.