Feedback Controllers as Financial Advisors for Low-Income Individuals

Feedback controllers are introduced to help manage an individual's or household's financial life and build savings. The controllers can be viewed as financial advisors for an individual's resource allocation problem, which is modeled as a nonlinear discrete time stochastic system with income uncertainties, asset losses, and constraints on cash flow and credit. We introduce a model predictive controller (MPC) and a proportional-integral-derivative (PID) controller, and compare them with a benchmark method employed in finance and economics, stochastic dynamic programming (DP). Both MPC and PID produce similar consistency in financial management compared with DP. They also offer the advantage of low computational complexity relative to DP, which allows us to efficiently perform assessments of robustness (reliability) and disturbance rejection (e.g., effects of uncertainties), both of which are of significant practical engineering importance. In addition, this flexibility enables us to uncover the system's properties, such as the existence of a “poverty trap” caused by constraints in the control space and dynamics. The effectiveness of a PID-based aid intervention for low-skilled and low-endowed agents that lie within the trap is assessed and contrasted with other existing cash transfer programs, with results that support a further implementation analysis. These assessments constitute a novel application of feedback controllers that, besides effectively dealing with scarcity constraints, present practical advantages that are shown to translate into an ability to implement the MPC or PID controller in a variety of ways for low-income individuals via computer-assistive methods (e.g., a cell phone).