The Analysis Of Insurance Contracts Model With An Upper Limit On Coverage And The Audit Of Having The Extent Of Efforts

Against the optimal deductibles and the insurance fraud problems in the insurance market, the paper, using the game theory as the major theoretical tools, is focus on the research of status and shortcoming of present works about it and constructs the model with an upper limit on coverage and the model with an audit having the extent of efforts.In the first part, this paper builds an insurance contract model with an upper limit on coverage and obtains the Nash equilibrium solution. This paper also examines the impact of the risk aversion, initial reserve and coverage limit to the behavior of the insurer and gains the sufficient condition of the impact of the risk aversion to the behavior of the insurer. It is shown that initial reserve turn out to have no effect on the behavior of the insurer with constant absolute risk aversion (CARA). The increase in the upper limit would induce the insurer with CARA to increase premium, and make the insured reduce his deductible and purchase more insurance.In the second part, the paper gives a model with the audit having the extent of efforts and deduces the optimal solution. The paper discusses the impact of the extent of the effort on the optimal contract. The insurer in fact selects the non-effort audit corresponding with the lower cost state to reduce the insurance cost when committing to auditing. The insured's expected marginal utility with respect to final wealth is the same in the accident state as in the no-accident state. Moreover, the paper concludes the conclusion that the insured deserves overcompensation in the high-loss state and undercompensation in the small-loss state, which is contrary to the common insurance contracts as we can see in the insurance market. The reason why there is few insurance contracts just mentioned above in the market is the insurer's consideration of the insurance cost and the ex ante moral hazard.