Positive Switching Systems and the Wealth Distribution Problem

Franco Blanchini; Daniele Casagrande; Patrizio Colaneri; Stefanny Ramirez; Dario Bauso

doi:10.1007/s10957-024-02579-z

Positive Switching Systems and the Wealth Distribution Problem

Franco Blanchini, Daniele Casagrande^*, Patrizio Colaneri, Stefanny Ramirez, Dario Bauso

^*Corresponding author for this work

Optimization and Decision Systems

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The paper shows how a dynamic model, belonging to the class of positive switching systems, can provide an interesting point of view to the study of the generation and the distribution of wealth in a society. In this model, the evolution of the overall wealth is affected by the way in which individuals share their resources in order to maximize the total income. Different formulations of the corresponding optimal control problem are considered and some general properties are pointed out. Approximated numerical solutions, as well as upper and lower bounds are also investigated. A final section dedicated to an extended numerical analysis yields some qualitative conclusion.

Original language	English
Article number	29
Number of pages	20
Journal	Journal of Optimization Theory and Applications
Volume	204
Issue number	2
DOIs	https://doi.org/10.1007/s10957-024-02579-z
Publication status	Published - Feb-2025

Keywords

Hamilton–Jacobi–Bellman equations
Lyapunov–Metzler equations
Optimal control
Pontryagin maximum principle
Positive switching systems

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title = "Positive Switching Systems and the Wealth Distribution Problem",

abstract = "The paper shows how a dynamic model, belonging to the class of positive switching systems, can provide an interesting point of view to the study of the generation and the distribution of wealth in a society. In this model, the evolution of the overall wealth is affected by the way in which individuals share their resources in order to maximize the total income. Different formulations of the corresponding optimal control problem are considered and some general properties are pointed out. Approximated numerical solutions, as well as upper and lower bounds are also investigated. A final section dedicated to an extended numerical analysis yields some qualitative conclusion.",

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author = "Franco Blanchini and Daniele Casagrande and Patrizio Colaneri and Stefanny Ramirez and Dario Bauso",

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AU - Blanchini, Franco

AU - Casagrande, Daniele

AU - Colaneri, Patrizio

AU - Ramirez, Stefanny

AU - Bauso, Dario

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

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Positive Switching Systems and the Wealth Distribution Problem

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