IDEAS home Printed from https://ideas.repec.org/p/flo/wpaper/2000-01.html
   My bibliography  Save this paper

Nonlinear effects in a discrete-time dynamic model of a stock market

Author

Listed:
  • Gian-Italo Bischi

    (Università di Urbino)

  • Vincenzo Valori

    (Dipartimento di Matematica per le Decisioni - Università degli Studi di Firenze)

Abstract

The time evolution of prices and savings in a stock market is modeled by a discrete time nonlinear dynamical system. The model proposed has a unique and unstable steady-state, so that the time evolution is determined by the nonlinear effects acting out of the equilibrium. The nonlinearities strongly influence the kind of long-run dynamics of the system. In particular, the global geometric properties of the noninvertible map of the plane, whose iteration gives the evolution of the system, are important to understand the global bifurcations which change the qualitative properties of the asymptotic dynamics. Such global bifurcations are studied by geometric and numerical methods based on the theory of critical curves, a powerful tool for the characterization of the global dynamical properties of noninvertible mappings of the plane. The model unfolds more complex chaotic and unpredictable trajectories as a consequence of increasing agents' "speculative" or "capital gain realizing" attitudes. The global analysis indicates that, for some ranges of the parameter values, the system has several coexisting attractors, and it may not be robust with respect to exogenous shocks due to the complexity of the basin of attraction.

Suggested Citation

  • Gian-Italo Bischi & Vincenzo Valori, 2000. "Nonlinear effects in a discrete-time dynamic model of a stock market," Working Papers - Mathematical Economics 2000-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    • Handle: RePEc:flo:wpaper:2000-01
    as

    Download full text from publisher

    File URL: http://www.disei.unifi.it/upload/sub/pubblicazioni/repec/flo/workingpapers/storicodimad/2000/dimadwp2000-01.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bischi, Gian-Italo & Stefanini, Luciano & Gardini, Laura, 1998. "Synchronization, intermittency and critical curves in a duopoly game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(6), pages 559-585.
    2. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, 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. Loretti I. Dobrescu & Dumitru Opris, 2008. "Hopf bifurcation and chaos analysis of a discrete-delay dynamic model for a stock market," "Marco Fanno" Working Papers 0082, Dipartimento di Scienze Economiche "Marco Fanno".
    2. Melecký, Jan & Sergyeyev, Artur, 2008. "A simple finite-difference stock market model involving intrinsic value," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 769-777.
    3. Loretti I. Dobrescu & Mihaela Neamtu & Dumitru Opris, 2011. "A Discrete--Delay Dynamic Model for the Stock Market," Discussion Papers 2012-11, School of Economics, The University of New South Wales.
    4. Matassini, Lorenzo, 2001. "The trading rectangle strategy within book models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 449-456.
    5. Matassini, Lorenzo & Franci, Fabio, 2001. "On financial markets trading," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 526-542.
    6. David Gray, 2014. "Central European foreign exchange markets: a cross-spectral analysis of the 2007 financial crisis," The European Journal of Finance, Taylor & Francis Journals, vol. 20(6), pages 550-567, June.
    7. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2462-2468.

    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. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, June.
    2. Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2014. "Local and global dynamics in a duopoly with price competition and market share delegation," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 253-270.
    3. Gori, Luca & Sodini, Mauro & Fanti, Luciano, 2015. "A nonlinear Cournot duopoly with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 178-190.
    4. Andrea Caravaggio & Lorenzo Cerboni Baiardi & Mauro Sodini, 2021. "A note on symmetry breaking in a non linear marketing model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 507-531, December.
    5. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    6. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    7. Caravaggio, Andrea & Gori, Luca & Sodini, Mauro, 2022. "Endogenous preferences in a dynamic Cournot duopoly," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    8. Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 166-177.
    9. Luís, Rafael & Mendonça, Sandra, 2024. "Local stability conditions for a n-dimensional periodic mapping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 15-30.
    10. Luciano Fanti & Luca Gori, 2013. "Stability Analysis in a Bertrand Duopoly with Different Product Quality and Heterogeneous Expectations," Journal of Industry, Competition and Trade, Springer, vol. 13(4), pages 481-501, December.
    11. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1469-1478.
    12. Fanti, Luciano & Gori, Luca, 2011. "The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited," MPRA Paper 33268, University Library of Munich, Germany.
    13. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2015. "Nonlinear dynamics in a Cournot duopoly with isoelastic demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 129-143.
    14. Dawid, Herbert, 2007. "Evolutionary game dynamics and the analysis of agent-based imitation models: The long run, the medium run and the importance of global analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 2108-2133, June.
    15. Joaquín Andaluz & Gloria Jarne, 2016. "Stability of vertically differentiated Cournot and Bertrand-type models when firms are boundedly rational," Annals of Operations Research, Springer, vol. 238(1), pages 1-25, March.
    16. Akio Matsumoto & Ferenc Szidarovszky & Keiko Nakayama, 2020. "Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model," Mathematics, MDPI, vol. 9(1), pages 1-19, December.
    17. Kamalinejad, Howra & Majd, Vahid Johari & Kebriaei, Hamed & Rahimi-Kian, Ashkan, 2010. "Cournot games with linear regression expectations in oligopolistic markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1874-1885.
    18. Ueda, Masahiko, 2019. "Effect of information asymmetry in Cournot duopoly game with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    19. Liu, Yuxia & Zhou, Wei & Wang, Qian, 2022. "Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    20. Bignami Fernando & Agliari Anna, 2010. "Synchronization and On-Off Intermittency Phenomena in a Market Model with Complementary Goods and Adaptive Expectations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(2), pages 1-31, March.

    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:flo:wpaper:2000-01. 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: Michele Gori (email available below). General contact details of provider: https://edirc.repec.org/data/defirit.html .

    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.