# The Interpretation and Application of 300 Years of Optimal Control in Economics

The Interpretation and Application of 300 Years of Optimal Control in Economics

AuthorSmit, Ruud (TU Delft Mechanical, Maritime and Materials Engineering; TU Delft Delft Center for Systems and Control)

Hellendoorn, Hans (graduation committee)

Mendel, Max (mentor)

Kop, Jochem (mentor)

Delft University of Technology

Programme Date2018-04-12

AbstractNeoclassical economics dictates the decision-making process of economic agents as the mathematical problem of maximizing utility over a prescribed planning horizon. The mathematical similarities with optimal control theory lead to a new interpretation of economic agents as optimal controllers. Pontryagin's maximum principle generates the necessary conditions, but the economic consequences become clear when its historical development is followed. It is found that the Euler-Lagrange equations result in a no-arbitrage condition in economics, and Hamilton's canonical equations describe the change in asset allocation and the asset price over time. The Hamiltonian itself is equivalent to the economic surplus of the agent, and the maximum principle requires that it is maximized along the optimal trajectory with respect to the control actions. This gives a different, myopic perspective to the economic agent, being an agent that maximizes economic surplus instantaneously instead of utility over an entire planning period.

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