Abstract: In this talk I will describe recent work in the analysis of an integro-differential equation used to model the risk process of a low income households. For this population, a proportional loss model is used to capture the catastrophic effects of income loss. These models are particularly adept for households with low liquidity, in which a governmental or NGO can provide subsidies for insurance. The mathematical analysis of the model combines stochastic processes, integro-differential equations and numerical calculations. This analysis helps determine conditions in which the insured population can avoid a certainty of ruin. The notion of speed and scale measures introduced by W Feller in his classical work on diffusions were used in the proof of properties of the solutions of the equations arising in this modeling. This is join work with Kira Henshaw, Jose Flores-Contro, Jorge Ramirez, Sooie-Hoe Loke and Coriina Constantinescu.