Ample evidence exists to suggest that nonlinear asset dynamics can give rise to an environment of poverty traps. When dynamic asset thresholds matter, risk not only affects households ex post, but it also influences ex ante behavior. In this environment some house-holds may have much to gain from a productive safety net which prevents asset levels from dipping below the Micawber threshold. Insurance is a market-based mechanism that can act as a safety net, improving the risk management strategies available to vulnerable households. In this paper we use dynamic programming methods to assess whether vulnerable households will `self-select' into an asset insurance scheme. We show that while such households opti- mally insure at low levels, insurance serves to crowd in additional investment, causing a shift in the Micawber threshold. This investment comes from the hope of reduced vulnerability that insurance offers in the future. Finally, we use our model to make predictions about the value of index-based livestock insurance (IBLI) in Marsabit district of northern Kenya. Our results suggest that the behavioral changes brought about by insurance may result in decreased poverty levels over time.