On the Impact of Insurance on Households Susceptible to Random Proportional Losses: An Analysis of Poverty Trapping

The trapping probability is studied for households' capital assuming that losses are proportional to the accumulated capital. We consider households without insurance and those purchasing proportional insurance. Parameter conditions under which poverty trapping is not certain in both cases are derived. For the uninsured model, a new closed-form expression for the trapping probability is obtained when the remaining proportion of capital after a loss has a beta distribution, showing that the trapping probability decays algebraically as the initial capital increases. When insurance is purchased and the remaining proportion is uniformly distributed, the trapping probability is computed by solving a non-local integro-differential equation. Our results show that insurance can prevent otherwise certain trapping in some cases, although it may increase trapping risk for households with initial capital barely above the poverty line, while reducing trapping risk for households with higher initial capital.