Background risk and consumers' demand for insurance under limited liability

This study highlights the importance of financial background risks in consumers' demand for coverage against insurable risks, considering the bankruptcy option. We explore three cases that are overlooked in theoretical literature, although found to be highly relevant in empirical studies: (1) the joint realization of the two financial risks is bankrupting, (2) the insurable risk is bankrupting and the background risk is not, and (3) each financial risk is bankrupting on its own. Our new results highlight the potential role of the background risk in decreasing demand for insurance (and thus insurance take‐up) and yield novel non‐monotonic relationships between the magnitude of the background risk and the demand for insurance coverage, given consumers' initial wealth. Our results align with recent empirical work that highlights the role of consumer bankruptcy as a substitute to formal health insurance, and thereby its significant negative effects on insurance take up among working‐age Americans.