Dynamic Programming Approach to Optimal Savings and Investment Decisions for Nigerian Households

Household savings and investment decisions in Nigeria are distorted by high inflation, shallow financial markets, limited insurance access, and income volatility that differs systematically across geographic zones and occupational categories. This study develops a dynamic programming model of optimal household consumption, savings, and portfolio allocation decisions over the life cycle, calibrated to empirical income and expenditure patterns of Nigerian households using the National Bureau of Statistics General Household Survey panel data for 2019 and 2022. The Bellman equation formulation accommodates income uncertainty modelled as a discrete Markov chain, a borrowing constraint reflecting limited household access to formal credit, and a portfolio choice between informal savings (esusu), bank deposits, and agricultural land investment. Value function iteration is used to solve the dynamic programme, with the state space discretised over wealth, income shock, and age dimensions. Simulated optimal decision rules are compared against observed household saving rates and portfolio compositions in the survey data. The model predicts that the borrowing constraint generates a significant precautionary savings motive, with constrained households saving 8.3 percentage points more of income than unconstrained households at the same income level. Portfolio simulations indicate that relaxing borrowing constraints increases welfare equivalent consumption by 6.1 percent for low-income rural households. Keywords: dynamic programming, household savings, life cycle model, Nigeria, precautionary savings.