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Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time.

Stefan Wrzaczek1, Michael Kuhn1, Ivan Frankovic1

  • 1Wittgenstein Centre (IIASA, VID/ÖAW, WU), Vienna Institute of Demography, Vienna, Austria.

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Summary
This summary is machine-generated.

This study transforms a multi-stage optimal control model with random switching into an age-structured model. This new approach offers a unified representation and simplifies numerical solutions for control dynamics.

Keywords:
Age-structured optimal control theoryCatastrophic disasterMulti-stageOptimal control theoryRandom switch

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Area of Science:

  • Optimal control theory
  • Mathematical modeling
  • Dynamic systems analysis

Background:

  • Multi-stage optimal control problems with random switching times present significant analytical challenges.
  • Traditional backward approaches can be complex and lack a unified representation of model stages.

Purpose of the Study:

  • To transform a multi-stage optimal control model with random switching time into an age-structured optimal control model.
  • To highlight the advantages of the proposed age-structured approach over standard backward methods.
  • To demonstrate the practical application of the new model in macroeconomic contexts.

Main Methods:

  • Mathematical transformation of a multi-stage optimal control model.
  • Development of an age-structured optimal control framework.
  • Application of numerical solution methods to the transformed model.

Main Results:

  • A compact and unified representation of the two model stages is achieved.
  • The age-structured model facilitates the application of well-known numerical solution techniques.
  • Clear illustration of state and control dynamics is provided.

Conclusions:

  • The age-structured optimal control model offers a more tractable and insightful alternative for problems with random switching.
  • The approach simplifies the analysis and numerical solution of complex dynamic systems.
  • The method is effective for illustrating macroeconomic dynamics, as shown in the provided example.