Should you be honest in reporting losses to your insurer?
Suppose that an unfortunate event occurred, resulting in losses to you, but fortunately, you are insured for such losses. So, should you report this loss event to your insurer to claim reimbursement? If you do, you will get certain indemnity payment as specified by the insurance contract, but you will be rated negatively and the premium next year will go up; if you do not, you will bear the entire loss on your own, but receive a “bonus” for keeping a clean history. This intrinsic tradeoff motivates us to formulate an intrapersonal game for an insured to study her loss reporting problem. We assume that the insured has purchased an insurance policy with full coverage, and the insurer adopts a bonus-malus system with two rate classes in pricing. For both risk-neutral and risk-averse insured, we obtain her equilibrium barrier strategy for reporting losses. The barrier is always equal in both classes and strictly positive, implying that the insured should hide “small” losses and only report “large” losses to the insurer.