Optimal Control with Heterogeneous Agents in Continuous Time

21 Pages Posted: 9 Nov 2013

Date Written: October 30, 2013

Abstract

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

Nuno, Galo, Optimal Control with Heterogeneous Agents in Continuous Time (October 30, 2013). ECB Working Paper No. 1608. Available at SSRN: https://ssrn.com/abstract=2347458

Galo Nuno (Contact Author)

Banco de España ( email )

Alcala 50
Madrid 28014
Spain

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