Effective Premium Discrimination For Designing Cyber Insurance Policies With Rare Losses

Cyber insurance like other types of insurance is a method of risk transfer, where the insured pays a premium in exchange for coverage in the event of a loss. As a result of the reduced risk for the insured and the lack of information on the insurer's side, the insured is generally inclined to lower its effort, leading to a worse state of security, a common phenomenon known as moral hazard. To mitigate moral hazard, a widely employed concept is premium discrimination, i.e., an agent/insured who exerts higher effort pays less premium. This, however, relies on the insurer's ability to assess the effort exerted by the insured. In this paper, we study two methods of premium discrimination that rely on two different types of assessment: pre-screening and post-screening. Pre-screening occurs before the insured enters into a contract and can be done at the beginning of each contract period; the result of this process gives the insurer an estimated risk on the insured, which then determines the contract terms. The post-screening mechanism involves at least two contract periods whereby the second-period premium is increased if a loss event occurs during the first period.Prior work shows that both pre-screening and post-screening are generally effective in mitigating moral hazard and increasing the insured's effort. The analysis in this study shows, however, that the conclusion becomes more nuanced when loss events are rare. Specifically, we show that post-screening is not effective at all with rare losses, while pre-screening can be an effective method when the agent perceives them as rarer than the insurer does; in this case pre-screening improves both the agent's effort level and the insurer's profit.