Equilibrium reporting strategy: Two rate classes and full insurance
研究在奖惩系统中，投保人购买全额保险后，为获取少报损失的好处而采用屏障策略，仅报告超过阈值的损失，并求解出风险中性和风险厌恶投保人的均衡报告策略，发现两个费率等级的均衡屏障相等且大于零，为事后道德风险提供理论解释。
Abstract We propose a multiperiod insurance model under a bonus–malus system with two rate classes and consider an insured who has purchased full insurance for her losses. To explore the potential advantage of underreporting her insurable losses, the insured follows a barrier strategy and only reports lossses above the barrier to the insurer. We obtain a unique equilibrium declaration strategy in closed form for a risk‐neutral insured who maximizes her expected wealth, and in semiclosed form for a risk‐averse insured who maximizes her expected exponential utility of wealth, both over an exogenous random horizon. We find that the equilibrium barriers for the two classes are equal and strictly greater than zero, offering a theoretical explanation for the underreporting of insurable losses, a form of ex post moral hazard. Finally, we consider the case of three rate classes and show, through numerical examples, that the equilibrium barriers are not equal.