In this seminar Akshay Shanker will provide an overview of his recent paper, Bellman without Berge: Maximum Theorem for Non-Compact Dynamic Problems.

Compactness and continuity are critical assumptions in standard dynamic programming theory. However, when a dynamic problem involves controlling a distribution of heterogeneous agents, the state-space becomes infinite dimensional. In problems with infinite dimensional state-spaces, compactness and continuity of feasibility correspondences can fail. In his paper, Akshay establishes a maximum theorem for infinite horizon optimisation problems with non-compact feasible correspondences. The maximum theorem can establish existence and compactness of optimal policies and continuity of value functions. The proof uses a new K-sup-compactness condition, which can be easily verified in economic models. The author applies the result to the problem of a planner maximising welfare subject to incomplete markets in an Aiyagari-Huggett model.

Akshay Shanker is a final year PhD student in economics at the Centre for Applied Macroeconomic Analysis (CAMA), Crawford School.

The CAMA Macroeconomics Brown Bag Seminars offer CAMA speakers, in particular PhD students, an opportunity to present their work in progress in front of their peers, and reputable visitors to showcase their work.