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Optimization in Age-Structured Dynamic Economic Models

Author

Listed:
  • Michael Freiberger

    (International Institute for Applied Systems Analysis (IIASA)
    Wittgenstein Center (IIASA, OeAW/VID, University of Vienna))

  • Michael Kuhn

    (International Institute for Applied Systems Analysis (IIASA)
    Wittgenstein Center (IIASA, OeAW/VID, University of Vienna)
    Vienna Institute of Demography)

  • Alexia Prskawetz

    (Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology
    Austrian Academy of Sciences
    International Institute for Applied Systems Analysis (IIASA)
    Wittgenstein Center (IIASA, OeAW/VID, University of Vienna))

  • Miguel Sanchez-Romero

    (Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology
    Austrian Academy of Sciences
    International Institute for Applied Systems Analysis (IIASA)
    Wittgenstein Center (IIASA, OeAW/VID, University of Vienna))

  • Stefan Wrzaczek

    (International Institute for Applied Systems Analysis (IIASA)
    Wittgenstein Center (IIASA, OeAW/VID, University of Vienna))

Abstract

Age-structured optimal control models experience increasing applications in various research fields including, e.g., demography, economics, operations research, epidemiology, and environmental economics. In this paper we present the mathematical theory and potential applications of age-structured optimal control models. We first state the general form of the problem and present the necessary optimality conditions. To illustrate the mathematical theory we introduce a toy model on air pollution, where consumption induces pollution which in turn negatively affects utility, fertility, and mortality. We solve the model analytically and present numerical simulations. The potential of an age-structure approach to solve non-standard optimal control models is demonstrated by considering optimal control models with random switches or time-lags and delays.

Suggested Citation

  • Michael Freiberger & Michael Kuhn & Alexia Prskawetz & Miguel Sanchez-Romero & Stefan Wrzaczek, 2025. "Optimization in Age-Structured Dynamic Economic Models," International Series in Operations Research & Management Science,, Springer.
    • Handle: RePEc:spr:isochp:978-3-031-88638-6_4
    DOI: 10.1007/978-3-031-88638-6_4
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