Solving the Income Fluctuation Problem with Unbounded Rewards
This page collects files and computer code for the paper Solving the Income Fluctuation Problem with Unbounded Rewards by Huiyu Li and John Stachurski.
This paper studies the income fluctuation problem without imposing bounds on utility, assets, income or consumption. We prove that the Coleman operator is a contraction mapping over the natural class of candidate consumption policies when endowed with a metric that evaluates consumption differences in terms of marginal utility. We show that this metric is complete, and that the fixed point of the operator coincides with the unique optimal policy. As a consequence, even in this unbounded setting, policy function iteration always converges to the optimal policy at a geometric rate.
Matlab code for replicating the numerical application can be found listed above.