Consumption–Saving with Uncertain Labor Income

This thesis delves into the numerical dynamic programming approach for addressing consumption and saving decisions under labor income uncertainty. The central objective is to ascertain optimal strategies for consumption and savings in the presence of two stochastic factors: varying labor conditions (modeled as unemployed, fully employed, and an intermediate state) and portfolio investment in both a riskless and a risky asset, with observed returns post-investment. Transitions between labor conditions are captured through a Markov chain. Utilizing Matlab scripts, the thesis employs a numerical dynamic programming framework, emphasizing scenario generation, value function approximation, and state space discretization. The overarching aim is to pinpoint the optimal strategy that maximizes a utility function linked to consumption, considering the dynamic interplay of wealth and employment conditions within the numerical dynamic programming paradigm.