Optimizing moral hazard management in health insurance through mathematical modeling of quasi-arbitrage

Moral hazard in health insurance arises when insured individuals are incentivized to over-utilize healthcare services, especially when they face low out-of-pocket costs. While existing literature primarily addresses moral hazard through qualitative studies, this paper introduces a quantitative approach by developing a mathematical model based on quasi-arbitrage conditions. The model optimizes health insurance design, focusing on the transition from Low-Deductible Health Plans (LDHPs) to High-Deductible Health Plans (HDHPs), and seeks to mitigate moral hazard by aligning the interests of both insurers and insured. Our analysis demonstrates how setting appropriate deductible levels and offering targeted premium reductions can encourage insured to adopt HDHPs while maintaining insurer profitability. The findings contribute to the theoretical framework of moral hazard mitigation in health insurance and offer actionable insights for policy design.