A stochastic model of group wealth responses to insurance mechanisms in low-income communities

This study addresses the group-based nature of financial vulnerability in the low-income environment. Adopting a highly flexible stochastic dissemination model, we assess the impact of insurance on the resilience of a low-income group to wealth shocks. For this purpose, the transient wealth of a group of interacting uninsured and insured agents is considered. The model is extended to capture four types of transaction events: external arrivals, internal redistributions, wealth losses and premium payments. Risk-sharing mechanisms, mitigating the impact of financial losses that are otherwise uninsured, are widespread in low-income communities. Our modelling of redistribution events captures the wealth transactions associated with these mechanisms, alongside the purchase of commodities and services from within the group. Through this set-up, we present a method for incorporating the high level of wealth interaction characteristic of the low-income setting in the assessment of the effectiveness of insurance. The model is underlined by an exogenously evolving Markov background process that represents the state of the economy. To analyse the distribution of wealth jointly with the state of the background process, a system of coupled differential equations for the joint transient distribution of agent wealth is derived, and is reduced to a linear system of differential equations through consideration of the moments of agent wealth. Sensitivity analysis is performed to establish the impact of the system's structure and stochastic dynamics on the wealth of the group. The probability of falling below the poverty line is then determined through application of a normal approximation and the impact of insurance in reducing this probability considered under varying levels of subsidisation.