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This paper develops a dynamic theoretical model to assess the impact of asset insurance on poverty and the cost of social protection in developing countries. We analyze the model under two technological assumptions: a standard, globally concave production technology, and a fixed cost technology that creates a non‐convex production set and admits the possibility of multiple equilibria and a poverty trap. Under both assumptions, the introduction of an asset insurance market reduces poverty and the costs of social protection. Under the non‐convex production set, there is a strong public finance case for insurance premium subsidies that target poor and vulnerable households and bring them into the insurance market. While the challenges of making microinsurance markets work are multiple, this analysis suggests the potential gains to solving these challenges are substantial.