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Fractal steady states instochastic optimal control models

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  • L. Montrucchio
  • F. Privileggi

Abstract

The paper is divided into two parts. We first extend the Boldrin and Montrucchio theorem[5] on the inverse control problem to the Markovian stochastic setting. Given a dynamicalsystem x t+1 =g(x t , z t ), we find a discount factor β * such that for each 0 > β > β * a concaveproblem exists for which the dynamical system is an optimal solution. In the second part,we use the previous result for constructing stochastic optimal control systems having fractalattractors. In order to do this, we rely on some results by Hutchinson on fractals and self‐similarities.A neo‐classical three‐sector stochastic optimal growth exhibiting the Sierpinskicarpet as the unique attractor is provided as an example. Copyright Kluwer Academic Publishers 1999

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  • L. Montrucchio & F. Privileggi, 1999. "Fractal steady states instochastic optimal control models," Annals of Operations Research, Springer, vol. 88(0), pages 183-197, January.
    • Handle: RePEc:spr:annopr:v:88:y:1999:i:0:p:183-197:10.1023/a:1018978213041
    DOI: 10.1023/A:1018978213041
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    Cited by:

    1. Guido Cozzi & Fabio Privileggi, 2009. "The fractal nature of inequality in a fast growing world: new version," Working Papers 2009_30, Business School - Economics, University of Glasgow.
    2. Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 110-129, August.
    3. La Torre, Davide & Marsiglio,Simone & Mendivil, Franklin & Privileggi, Fabio, 2023. "Stochastic Optimal Growth through State-Dependent Probabilities," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202312, University of Turin.
    4. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    5. Davide Torre & Simone Marsiglio & Franklin Mendivil & Fabio Privileggi, 2024. "Stochastic disease spreading and containment policies under state-dependent probabilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 127-168, February.
    6. Yuxin Zhao & Shuai Chang & Chang Liu, 2015. "Multifractal theory with its applications in data management," Annals of Operations Research, Springer, vol. 234(1), pages 133-150, November.
    7. Simone Marsiglio & Privileggi, Fabio, 2020. "Three Dimensional Fractal Attractors in a Green Transition Economic Growth Model," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202019, University of Turin.
    8. La Torre, Davide & Marsiglio, Simone & Privileggi, Fabio, 2018. "Fractal Attractors in Economic Growth Models with Random Pollution Externalities," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201801, University of Turin.
    9. La Torre Davide & Rocca Matteo, 2002. "Approximating continuous functions by iterated function systems and optimization problems," Economics and Quantitative Methods qf0206, Department of Economics, University of Insubria.
    10. Stefano Maria Iacus & Davide La Torre, 2002. "Approximating distribution functions by iterated function systems," Departmental Working Papers 2002-03, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    11. Tapan Mitra & Luigi Montrucchio & Fabio Privileggi, 2003. "The nature of the steady state in models of optimal growth under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 39-71, December.
    12. Guido Cozzi & Fabio Privileggi, 2002. "Wealth Polarization and Pulverization in Fractal Societies," ICER Working Papers - Applied Mathematics Series 39-2002, ICER - International Centre for Economic Research.
    13. Davide La Torre & Matteo Rocca, 2002. "Approximating continuous functions by iterated function system and optimization," Departmental Working Papers 2002-11, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    14. Mitra, Tapan & Privileggi, Fabio, 2003. "Cantor Type Invariant Distributions in the Theory of Optimal Growth under Uncertainty," Working Papers 03-09, Cornell University, Center for Analytic Economics.
    15. Torre, Davide La & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2019. "A stochastic economic growth model with health capital and state-dependent probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 81-93.
    16. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.
    17. Davide LA TORRE, 2001. "On inverse problems for iterated function systems," Departmental Working Papers 2001-11, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    18. Mitra, Tapan & Privileggi, Fabio, 2006. "Cantor type attractors in stochastic growth models," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 626-637.
    19. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2016. "Fractal Attractors and Singular Invariant Measures in Two-Sector Growth Models with Random Factor Shares," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201620, University of Turin.
    20. La Torre, Davide & Marsiglio, Simone & Privileggi, Fabio, 2011. "Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model," POLIS Working Papers 157, Institute of Public Policy and Public Choice - POLIS.
    21. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2021. "Generalized Fractal Transforms with Condensation: a Macroeconomic-Epidemiological Application," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202107, University of Turin.
    22. Klaus Reiner Schenk-Hopp�, "undated". "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
    23. Guido Cozzi & Fabio Privileggi, 2007. "The Fractal Nature of Inequality in a Fast Growing World," Working Papers 2007_45, Business School - Economics, University of Glasgow.

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