Positive Switching Systems and the Wealth Distribution Problem

Franco Blanchini (), Daniele Casagrande (), Patrizio Colaneri (), Stefanny Ramirez () and Dario Bauso ()
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Franco Blanchini: Università degli Studi di Udine
Daniele Casagrande: Università degli Studi di Udine
Patrizio Colaneri: Politecnico di Milano
Stefanny Ramirez: University of Groningen
Dario Bauso: University of Groningen

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 2, No 14, 20 pages

Abstract: 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.

Keywords: Optimal control; Positive switching systems; Hamilton–Jacobi–Bellman equations; Lyapunov–Metzler equations; Pontryagin maximum principle (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02579-z

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