We study a strategic loss reporting problem for an insured who seeks an optimal strategy to dictate what losses she should report to the insurer, with the purpose to maximize her expected wealth (risk-neutral case) or expected utility of wealth (risk-averse case). To explore the potential advantage of underreporting her insurable losses, the insured follows a barrier strategy and only reports losses above the barrier to the insurer. Under a tractable 2-class bonus-malus model and given that the insured has purchased full insurance, we obtain a unique equilibrium reporting strategy in (semi)closed form. We find that the two equilibrium barriers are the same and strictly greater than zero, offering a theoretical explanation for the underreporting of insurable losses. If time allows, we will discuss the generalization to the case where the insured has deductible insurance and may even take into account strategic reporting in the decision of contract deductibles.
This talk is based on joint work with Jingyi Cao, Dongchen Li, and Jenny Young.