Theoretically, wealthier people should buy less insurance, and should self-insure through saving instead, as insurance entails monitoring costs. Here, we use administrative data for 63,000 individuals and, contrary to theory, find that the wealthier have better life and property insurance coverage. Wealth-related differences in background risk, legal risk, liquidity constraints, financial literacy, and pricing explain only a small fraction of the positive wealth-insurance correlation. This puzzling correlation persists in individual fixed-effects models estimated using 2.5 million person-month observations. The fact that the less wealthy have less coverage, though intuitively they benefit more from insurance, might increase financial health disparities among households.