[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/zur/iewwpx/067.html
   My bibliography  Save this paper

Random Dynamical Systems in Economics

Author

Listed:
  • Klaus Reiner Schenk-Hopp�
Abstract
This paper surveys recent advances in the application of random dy- namical systems theory in economics. It illustrates the usefulness of this framework for modeling and analysis of economic phenomena with stochastic components, mainly focusing on stochastic dynamic models in economic growth. The paper also highlights some directions for further applications and interdisciplinary research on random dynamical systems.

Suggested Citation

  • Klaus Reiner Schenk-Hopp�, "undated". "Random Dynamical Systems in Economics," IEW - Working Papers 067, Institute for Empirical Research in Economics - University of Zurich.
    • Handle: RePEc:zur:iewwpx:067
    as

    Download full text from publisher

    File URL: https://www.zora.uzh.ch/id/eprint/51968/1/iewwp067.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-781, July.
    2. Schenk-Hoppe, Klaus Reiner & Schmalfu[ss], Bjorn, 2001. "Random fixed points in a stochastic Solow growth model," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 19-30, September.
    3. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    4. Alos-Ferrer, Carlos & Ania, Ana B. & Schenk-Hoppe, Klaus Reiner, 2000. "An Evolutionary Model of Bertrand Oligopoly," Games and Economic Behavior, Elsevier, vol. 33(1), pages 1-19, October.
    5. Schenk-Hoppe, Klaus Reiner, 2000. "The evolution of Walrasian behavior in oligopolies," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 35-55, February.
    6. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    7. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    8. Leonard J. Mirman & Klaus Reiner Schenk‐Hoppé, 2003. "Financial Markets and Stochastic Growth," Review of International Economics, Wiley Blackwell, vol. 11(2), pages 219-236, May.
    9. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    10. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    11. Ragnar Frisch, 1936. "On the Notion of Equilibrium and Disequilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 3(2), pages 100-105.
    12. Ulrich Witt, 1994. "Evolutionary economics," Chapters, in: Peter J. Boettke (ed.), The Elgar Companion to Austrian Economics, chapter 78, Edward Elgar Publishing.
    13. L. Montrucchio & F. Privileggi, 1999. "Fractal steady states instochastic optimal control models," Annals of Operations Research, Springer, vol. 88(0), pages 183-197, January.
    14. Spear, Stephen E. & Srivastava, Sanjay, 1986. "Markov rational expectations equilibria in an overlapping generations model," Journal of Economic Theory, Elsevier, vol. 38(1), pages 35-62, February.
    15. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831, Elsevier.
    16. Tapan Mitra & Gerhard Sorger, 1999. "Rationalizing Policy Functions by Dynamic Optimization," Econometrica, Econometric Society, vol. 67(2), pages 375-392, March.
    17. Ulrich Witt, 1992. "Evolutionary Concepts in Economics," Eastern Economic Journal, Eastern Economic Association, vol. 18(4), pages 405-419, Fall.
    18. Wang Yong, 1993. "Stationary Equilibria in an Overlapping Generations Economy with Stochastic Production," Journal of Economic Theory, Elsevier, vol. 61(2), pages 423-435, December.
    19. repec:bla:ecorec:v:78:y:2002:i:243:p:375-80 is not listed on IDEAS
    20. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922, Elsevier.
    21. Grandmont, Jean-Michel & Hildenbrand, Werner, 1974. "Stochastic processes of temporary equilibria," Journal of Mathematical Economics, Elsevier, vol. 1(3), pages 247-277, December.
    22. Mirman, Leonard J, 1972. "On the Existence of Steady State Measures for One Sector Growth Models with Uncertain Technology," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(2), pages 271-286, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Firoozi, Fathali, 2006. "On the martingale property of economic and financial instruments," International Review of Economics & Finance, Elsevier, vol. 15(1), pages 87-96.
    2. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2008. "Evolutionary Finance," Swiss Finance Institute Research Paper Series 08-14, Swiss Finance Institute.
    3. Igor Evstigneev & Thorsten Hens & Klaus Schenk-Hoppé, 2006. "Evolutionary stable stock markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 449-468, January.
    4. Igor V. EVSTIGNEEVY & Thorsten HENS & Klaus Reiner SCHENK-HOPPE, 2010. "An evolutionary financial market model with a risk-free asset," Swiss Finance Institute Research Paper Series 10-36, Swiss Finance Institute.
    5. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
    6. Thorsten Hens & Klaus Schenk-Hopp�, "undated". "Evolution of Portfolio Rules in Incomplete Markets," IEW - Working Papers 074, Institute for Empirical Research in Economics - University of Zurich.
    7. Olkhov, Victor, 2016. "On Economic Space notion," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 372-381.
    8. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, 2006. "Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den," Faculty Working Papers 13/06, School of Economics and Business Administration, University of Navarra.
    9. Schenk-Hoppe, Klaus Reiner, 2005. "Poverty traps and business cycles in a stochastic overlapping generations economy with S-shaped law of motion," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 275-288, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Schenk-Hoppe, Klaus Reiner & Schmalfu[ss], Bjorn, 2001. "Random fixed points in a stochastic Solow growth model," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 19-30, September.
    2. Takeoka, Norio, 2006. "Stationary Markov equilibria on a non-compact self-justified set," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 269-290, June.
    3. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
    4. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    5. Jaime McGovern & Olivier Morand & Kevin Reffett, 2013. "Computing minimal state space recursive equilibrium in OLG models with stochastic production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 623-674, November.
    6. Takeoka, Norio, 2003. "On the consistency of stationary Markov equilibria with an exogenous distribution," Journal of Economic Theory, Elsevier, vol. 113(2), pages 316-324, December.
    7. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    8. 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.
    9. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, April.
    10. Athreya, Kartik B., 2014. "Big Ideas in Macroeconomics: A Nontechnical View," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262019736, April.
    11. repec:ebl:ecbull:v:3:y:2008:i:41:p:1-14 is not listed on IDEAS
    12. Jonas Hedlund, 2015. "Imitation in Cournot oligopolies with multiple markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 567-587, November.
    13. Mandel, Antoine & Gintis, Herbert, 2016. "Decentralized Pricing and the equivalence between Nash and Walrasian equilibrium," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 84-92.
    14. Juan Sebastián Pereyra & Juan Gabriel Brida, 2008. "The Solow model in discrete time and decreasing population growth rate," Economics Bulletin, AccessEcon, vol. 3(41), pages 1-14.
    15. Darong Dai, 2014. "A Golden Formula in Neoclassical-Growth Models with Brownian-Motion Shocks," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(2), pages 211-228, May.
    16. Edward C. Prescott, 1986. "Theory ahead of business cycle measurement," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 10(Fall), pages 9-22.
    17. 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.
    18. Böhm, Volker & Wenzelburger, Jan, 2002. "Perfect Predictions In Economic Dynamical Systems With Random Perturbations," Macroeconomic Dynamics, Cambridge University Press, vol. 6(5), pages 687-712, November.
    19. Hehenkamp, Burkhard & Wambach, Achim, 2010. "Survival at the center--The stability of minimum differentiation," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 853-858, December.
    20. Alos-Ferrer, Carlos, 2004. "Cournot versus Walras in dynamic oligopolies with memory," International Journal of Industrial Organization, Elsevier, vol. 22(2), pages 193-217, February.
    21. Ana Paula MARTINS, 2016. "Wealth-In-Utility and Time-Consistent Growth: Real Excursions with an “Overlapping” Welfare Function," Turkish Economic Review, KSP Journals, vol. 3(1), pages 54-81, March.

    More about this item

    Keywords

    random dynamical systems; dynamic models; economic growth;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zur:iewwpx:067. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Severin Oswald (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.