Optimal Control with Heterogeneous Agents in Continuous Time
21 Pages Posted: 9 Nov 2013
Date Written: October 30, 2013
This paper introduces the problem of a planner who wants to control a population of heterogeneous agents subject to idiosyncratic shocks. The agents differ in their initial states and in the realization of the shocks. In continuous time, the distribution of states across agents is described by a Kolmogorov forward equation. The planner chooses the controls in order to maximize an optimality criterion subject to an "aggregate resource constraint". We demonstrate how the solution should satisfy a system of partial differential equations that includes a generalization of the Hamilton-Jacobi-Bellman equation and the Kolmogorov forward equation.
Keywords: Kolmogorov forward equation, calculus of variations, dynamic programming, heterogeneous agents
JEL Classification: C6, D3, D5, E2
Suggested Citation: Suggested Citation