Analysis of insurance contract with the auditing efforts

Depending on the game theory and the hypothesis that the insured's auditing efforts could be measured, the paper analyses the problem that the insured often exaggerate the loss state to extract more compensation in the insurance market, and leads to the optimal insurance contract model and the optimal solution. Because of the auditing cost, the insurer's optimal auditing strategy is the no-effort-auditing strategy, not the effort-auditing strategy. 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 deserve overcompensation in the high-loss state and undercompensation in the low-loss state, which is contrary to the common insurance contracts as we can see in the insurance market.