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<p>The paper studies an economic growth model with phase constraints in terms of the probability theory. Main model factors which are restricted by the phase constraints can be interpreted as a&#xa0;probability function and density of some random variable. A class of probability distribution is selected using qualitative properties of the optimal solutions, previously derived for the studied problem statement within the Pontryagin maximum principle. The work performs the identification of the distribution parameters and the constructs admissible solutions of the problem by investigating probability characteristics of the random variable. Finally, the trends for all model variables are derived through the constructed solutions including the elements of the utility function.</p>

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An admissible solution of the growth problem with phase constraints based on the logistic distribution

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Anastasiia A. Usova,
  • Alexander M. Tarasyev

摘要

The paper studies an economic growth model with phase constraints in terms of the probability theory. Main model factors which are restricted by the phase constraints can be interpreted as a probability function and density of some random variable. A class of probability distribution is selected using qualitative properties of the optimal solutions, previously derived for the studied problem statement within the Pontryagin maximum principle. The work performs the identification of the distribution parameters and the constructs admissible solutions of the problem by investigating probability characteristics of the random variable. Finally, the trends for all model variables are derived through the constructed solutions including the elements of the utility function.