Arrow and Lind (1970) showed that governments can evaluate public investments as if risk-neutral when losses spread across a large, diversified tax base. This paper formalizes what happens as those conditions erode. Relaxing the theorem's assumptions traces a severity continuum: the optimal policy transitions from pure self-insurance through portfolios of financial instruments and physical mitigation to a disaster trap where no feasible combination prevents fiscal collapse. The continuum is indexed by 1 poverty traps (Carter and Barrett, 2006)-through a single Bellman equation. Calibration to a U.S. Gulf Coast county and a Pacific island state produces quantitatively meaningful results from the same equation, differing only in parameter values.