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Optimal Control Theory with Applications in Economics

Author

Listed:
  • Weber, Thomas A.

    (Swiss Federal Institute of Technology)

Abstract

This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.

Suggested Citation

  • Weber, Thomas A., 2011. "Optimal Control Theory with Applications in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015730, December.
    • Handle: RePEc:mtp:titles:0262015730
    as

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    Citations

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    Cited by:

    1. Pierre Bernhard & Marc Deschamps, 2017. "Kalman on dynamics and contro, Linear System Theory, Optimal Control, and Filter," Working Papers 2017-10, CRESE.
    2. Weber, Thomas A., 2014. "On the (non-)equivalence of IRR and NPV," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 25-39.
    3. Kozlov, Roman, 2021. "An age-structured model for the effect of interest rate changes on consumption," Discussion Papers 2021/8, Norwegian School of Economics, Department of Business and Management Science.
    4. Avinadav, Tal & Chernonog, Tatyana & Khmelnitsky, Eugene, 2021. "Revenue-sharing between developers of virtual products and platform distributors," European Journal of Operational Research, Elsevier, vol. 290(3), pages 927-945.
    5. Christopher W. Miller & Insoon Yang, 2015. "Optimal Dynamic Contracts for a Large-Scale Principal-Agent Hierarchy: A Concavity-Preserving Approach," Papers 1506.05497, arXiv.org.
    6. David van Wijk, 2023. "Stochastic Control Barrier Functions for Economics," Papers 2312.12612, arXiv.org, revised Feb 2024.
    7. Alagoz, B. Baykant & Kaygusuz, Asim & Akcin, Murat & Alagoz, Serkan, 2013. "A closed-loop energy price controlling method for real-time energy balancing in a smart grid energy market," Energy, Elsevier, vol. 59(C), pages 95-104.
    8. Song, Jae Eun, 2014. "Competitive Search Equilibrium in the Credit Market under Asymmetric Information and Limited Commitment," MPRA Paper 57515, University Library of Munich, Germany.
    9. Angel Sanchis-Cano & Luis Guijarro & Massimo Condoluci, 2018. "Dynamic capacity provision for wireless sensors’ connectivity: A profit optimization approach," International Journal of Distributed Sensor Networks, , vol. 14(4), pages 15501477187, April.
    10. Thomas A. Weber, 2017. "Global Optimization on an Interval," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 684-705, February.
    11. Virtue U. Ekhosuehi, 2021. "Optimal control of external debt for a developing economy," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 889-905, December.
    12. Liviu Popescu & Daniel Militaru & Gabriel Tică, 2022. "Lie Geometric Methods in the Study of Driftless Control Affine Systems with Holonomic Distribution and Economic Applications," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    13. Thomas A. Weber, 2017. "Optimal switching between cash-flow streams," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 567-600, December.
    14. Thomas A. Weber, 2016. "A robust resolution of Newcomb’s paradox," Theory and Decision, Springer, vol. 81(3), pages 339-356, September.
    15. Silvia Bertarelli & Chiara Lodi & Stefania Ragni, 2022. "An optimal strategy to control mining and recycling of non-renewable resources," Working Papers 2202, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2022.
    16. Julia Eisenberg & Peter Grandits & Stefan Thonhauser, 2014. "Optimal Consumption Under Deterministic Income," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 255-279, January.
    17. Weber, Thomas A., 2014. "A continuum of commitment," Economics Letters, Elsevier, vol. 124(1), pages 67-73.
    18. Natalia Aizenberg & Nikolai Voropai, 2021. "The Optimal Mechanism Design of Retail Prices in the Electricity Market for Several Types of Consumers," Mathematics, MDPI, vol. 9(10), pages 1-25, May.
    19. Chih-Chun KUNG, 2018. "A dynamic framework of sustainable development in agriculture and bioenergy," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 64(10), pages 445-455.
    20. Naveed Chehrazi & Peter W. Glynn & Thomas A. Weber, 2019. "Dynamic Credit-Collections Optimization," Management Science, INFORMS, vol. 67(6), pages 2737-2769, June.
    21. Naveed Chehrazi & Lauren E. Cipriano & Eva A. Enns, 2019. "Dynamics of Drug Resistance: Optimal Control of an Infectious Disease," Operations Research, INFORMS, vol. 67(3), pages 619-650, May.

    More about this item

    Keywords

    optimal control theory; game theory; economic theory; decision making; modeling;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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