Equilibrium Loss Reporting for a Risk-Averse Insured of Deductible Insurance
24 Pages Posted: 23 Aug 2023
Abstract
We consider a risk-averse insured who purchases a deductible insurance contract and follows a barrier strategy to decide whether she should report a loss. The insurer adopts a bonus-malus system with two rate classes, and the insured will move to or stay in the more expensive class if she reports a loss. When the deductibles are exogenously given, we establish a sufficient and necessary condition under which the insured will underreport losses, and obtain her equilibrium barrier strategy in semi-closed form. Next, we allow the insured to choose the deductibles of her insurance contract and numerically show that the equilibrium deductibles are strictly positive, suggesting that full insurance, often assumed in related literature, is not optimal. Our study justifies the prevalent phenomenon of underreporting losses across non-life insurance sectors.
Keywords: moral hazard, underreporting losses, deductible insurance, bonus-malus system, Nash equilibrium
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