IDEAS home Printed from https://ideas.repec.org/a/spr/decfin/v41y2018i2d10.1007_s10203-018-0214-3.html
   My bibliography  Save this article

Steady states, stability and bifurcations in multi-asset market models

Author

Listed:
  • Roberto Dieci

    (University of Bologna)

  • Noemi Schmitt

    (University of Bamberg)

  • Frank Westerhoff

    (University of Bamberg)

Abstract

We provide a full analytical treatment of a multi-asset market model in which speculators have the choice between two risky and one safe asset. As it turns out, the dynamics of our model is driven by a four-dimensional nonlinear map and may undergo a transcritical, flip or Neimark–Sacker bifurcation. While the first bifurcation is associated with an undervaluation of the risky assets, the latter two may trigger (complex) endogenous dynamics. To facilitate our analysis, we first study a simpler two-dimensional setup of our model in which speculators can only switch between one risky and one safe asset.

Suggested Citation

  • Roberto Dieci & Noemi Schmitt & Frank Westerhoff, 2018. "Steady states, stability and bifurcations in multi-asset market models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 357-378, November.
    • Handle: RePEc:spr:decfin:v:41:y:2018:i:2:d:10.1007_s10203-018-0214-3
    DOI: 10.1007/s10203-018-0214-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10203-018-0214-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10203-018-0214-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hommes, Cars & Lustenhouwer, Joep, 2019. "Managing unanchored, heterogeneous expectations and liquidity traps," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 1-16.
    2. Schmitt, Noemi & Westerhoff, Frank, 2014. "Speculative behavior and the dynamics of interacting stock markets," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 262-288.
    3. Noemi Schmitt & Frank Westerhoff, 2017. "Heterogeneity, spontaneous coordination and extreme events within large-scale and small-scale agent-based financial market models," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1041-1070, November.
    4. Quis, Johanna Sophie & Reif, Simon, 2017. "Health effects of instruction intensity: Evidence from a natural experiment in German high-schools," FAU Discussion Papers in Economics 12/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    5. Shleifer, Andrei & Summers, Lawrence H, 1990. "The Noise Trader Approach to Finance," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 19-33, Spring.
    6. González-Díaz, Julio & Herold, Florian & Domínguez, Diego, 2016. "Strategic sequential voting," BERG Working Paper Series 113, Bamberg University, Bamberg Economic Research Group.
    7. Herber, Stefanie P. & Kalinowski, Michael, 2016. "Non-take-up of student financial aid: A microsimulation for Germany," BERG Working Paper Series 109, Bamberg University, Bamberg Economic Research Group.
    8. March, Christoph & Sahm, Marco, 2018. "Contests as selection mechanisms: The impact of risk aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 114-131.
    9. Schmitt, Noemi & Tuinstra, Jan & Westerhoff, Frank, 2017. "Side effects of nonlinear profit taxes in an evolutionary market entry model: Abrupt changes, coexisting attractors and hysteresis problems," Journal of Economic Behavior & Organization, Elsevier, vol. 135(C), pages 15-38.
    10. Hommes, Cars & Lustenhouwer, Joep & Mavromatis, Kostas, 2018. "Fiscal consolidations and heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 173-205.
    11. Noemi Schmitt & Jan Tuinstra & Frank Westerhoff, 2018. "Stability and welfare effects of profit taxes within an evolutionary market interaction model," Review of International Economics, Wiley Blackwell, vol. 26(3), pages 691-708, August.
    12. Laica, Christoph & Lauber, Arne & Sahm, Marco, 2017. "Sequential round-robin tournaments with multiple prizes," BERG Working Paper Series 129, Bamberg University, Bamberg Economic Research Group.
    13. Westerhoff, Frank H. & Dieci, Roberto, 2006. "The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 293-322, February.
    14. Sahm, Marco, 2017. "Are sequential round-robin tournaments discriminatory?," BERG Working Paper Series 121, Bamberg University, Bamberg Economic Research Group.
    15. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    16. Blaurock, Ivonne & Schmitt, Noemi & Westerhoff, Frank, 2018. "Market entry waves and volatility outbursts in stock markets," Journal of Economic Behavior & Organization, Elsevier, vol. 153(C), pages 19-37.
    17. Lena Dräger & Christian R. Proaño, 2015. "Cross-Border Banking and Business Cycles in Asymmetric Currency Unions," Macroeconomics and Finance Series 201501, University of Hamburg, Department of Socioeconomics.
    18. March, Christoph & Sahm, Marco, 2017. "Asymmetric discouragement in asymmetric contests," Economics Letters, Elsevier, vol. 151(C), pages 23-27.
    19. Christian Menden & Christian R. Proaño, 2017. "Dissecting the financial cycle with dynamic factor models," Quantitative Finance, Taylor & Francis Journals, vol. 17(12), pages 1965-1994, December.
    20. Silke Anger & Daniel D. Schnitzlein, 2017. "Cognitive skills, non-cognitive skills, and family background: evidence from sibling correlations," Journal of Population Economics, Springer;European Society for Population Economics, vol. 30(2), pages 591-620, April.
    21. Schmitt, Noemi, 2018. "Heterogeneous expectations and asset price dynamics," BERG Working Paper Series 134, Bamberg University, Bamberg Economic Research Group.
    22. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    23. Flaschel, Peter & Charpe, Matthieu & Galanis, Giorgos & Proaño, Christian R. & Veneziani, Roberto, 2018. "Macroeconomic and stock market interactions with endogenous aggregate sentiment dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 237-256.
    24. Stefanie P. Herber & Michael Kalinowski, 2016. "Non-Take-Up of Student Financial Aid: A Microsimulation for Germany," SOEPpapers on Multidisciplinary Panel Data Research 844, DIW Berlin, The German Socio-Economic Panel (SOEP).
    25. Herold, Florian & Kuzmics, Christoph, 2020. "The evolution of taking roles," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 38-63.
    26. Marco Sahm, 2017. "Risk aversion and prudence in contests," Economics Bulletin, AccessEcon, vol. 37(2), pages 1122-1132.
    27. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    28. Lisa Planer-Friedrich & Marco Sahm, 2017. "Strategic Corporate Social Responsibility," CESifo Working Paper Series 6506, CESifo.
    29. De Long, J Bradford, et al, 1990. "Positive Feedback Investment Strategies and Destabilizing Rational Speculation," Journal of Finance, American Finance Association, vol. 45(2), pages 379-395, June.
    30. Planer-Friedrich, Lisa & Sahm, Marco, 2016. "Why firms should care for all consumers," BERG Working Paper Series 116, Bamberg University, Bamberg Economic Research Group.
    31. Viinikainen, Jutta & Heineck, Guido & Böckerman, Petri & Hintsanen, Mirka & Raitakari, Olli & Pehkonen, Jaakko, 2016. "Born entrepreneur? Adolescents' personality characteristics and self-employment in adulthood," BERG Working Paper Series 108, Bamberg University, Bamberg Economic Research Group.
    32. Marco Sahm, 2017. "Risk Aversion and Prudence in Contests," CESifo Working Paper Series 6417, CESifo.
    33. Agliari, Anna & Naimzada, Ahmad & Pecora, Nicolò, 2018. "Boom-bust dynamics in a stock market participation model with heterogeneous traders," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 458-468.
    34. Agliari, Anna & Dieci, Roberto & Gardini, Laura, 2007. "Homoclinic tangles in a Kaldor-like business cycle model," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 324-347, March.
    35. Carl Chiarella & Roberto Dieci & Laura Gardini, 2005. "The Dynamic Interaction of Speculation and Diversification," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 17-52.
    36. Chiarella, Carl & Dieci, Roberto & He, Xue-Zhong, 2007. "Heterogeneous expectations and speculative behavior in a dynamic multi-asset framework," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 408-427, March.
    37. Schmitt, Noemi & Westerhoff, Frank, 2015. "Managing rational routes to randomness," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 157-173.
    38. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    39. Robert J. Shiller, 2015. "Irrational Exuberance," Economics Books, Princeton University Press, edition 3, number 10421.
    40. Christoph Laica & Arne Lauber & Marco Sahm, 2017. "Sequential Round-Robin Tournaments with Multiple Prizes," CESifo Working Paper Series 6685, CESifo.
    41. Herber, Stefanie P. & Kalinowski, Michael, 2016. "Non-take-up of Student Financial Aid: A Microsimulation for Germany," VfS Annual Conference 2016 (Augsburg): Demographic Change 145727, Verein für Socialpolitik / German Economic Association.
    42. Pietro Dindo & Jan Tuinstra, 2011. "A Class of Evolutionary Models for Participation Games with Negative Feedback," Computational Economics, Springer;Society for Computational Economics, vol. 37(3), pages 267-300, March.
    43. Dieci, Roberto & Schmitt, Noemi & Westerhoff, Frank, 2018. "Interactions between stock, bond and housing markets," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 43-70.
    44. Lojak, Benjamin, 2016. "Sentiment-driven investment, non-linear corporate debt dynamics and co-existing business cycle regimes," BERG Working Paper Series 112, Bamberg University, Bamberg Economic Research Group.
    45. Sahm, Marco, 2017. "Are Sequential Round-Robin Tournaments Discriminatory?," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168113, Verein für Socialpolitik / German Economic Association.
    46. Sahm, Marco, 2016. "Advance-purchase financing of projects with few buyers," BERG Working Paper Series 118, Bamberg University, Bamberg Economic Research Group.
    47. Shiller, Robert J, 1990. "Speculative Prices and Popular Models," Journal of Economic Perspectives, American Economic Association, vol. 4(2), pages 55-65, Spring.
    48. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    49. Sahm, Marco, 2017. "Risk aversion and prudence in contests," BERG Working Paper Series 120, Bamberg University, Bamberg Economic Research Group.
    50. Shleifer, Andrei & Vishny, Robert W, 1997. "The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
    51. Noemi Schmitt & Frank Westerhoff, 2017. "Herding behaviour and volatility clustering in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1187-1203, August.
    52. Schmitt, Noemi & Westerhoff, Frank, 2018. "Evolutionary Competition And Profit Taxes: Market Stability Versus Tax Burden," Macroeconomic Dynamics, Cambridge University Press, vol. 22(8), pages 2007-2031, December.
    53. Schmitt, Noemi & Westerhoff, Frank, 2016. "Stock market participation and endogenous boom-bust dynamics," Economics Letters, Elsevier, vol. 148(C), pages 72-75.
    54. Planer-Friedrich, Lisa & Sahm, Marco, 2017. "Strategic corporate social responsibility," BERG Working Paper Series 124, Bamberg University, Bamberg Economic Research Group.
    55. Marco Sahm, 2017. "Are Sequential Round-Robin Tournaments Discriminatory?," CESifo Working Paper Series 6421, CESifo.
    56. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    57. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    58. Lustenhouwer, Joep & Mavromatis, Kostas, 2017. "Fiscal consolidations and finite planning horizons," BERG Working Paper Series 130, Bamberg University, Bamberg Economic Research Group.
    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. Christoph March & Marco Sahm, 2019. "The Perks of Being in the Smaller Team: Incentives in Overlapping Contests," CESifo Working Paper Series 7994, CESifo.
    2. Nivedita Mukherji, 2022. "Complex dynamics in the market for loans," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 83-99, June.
    3. Arata, Yoshiyuki & Mundt, Philipp, 2019. "Topology and formation of production input interlinkages: Evidence from Japanese microdata," BERG Working Paper Series 152, Bamberg University, Bamberg Economic Research Group.
    4. Mundt, Philipp & Oh, Ilfan, 2019. "Asymmetric competition, risk, and return distribution," BERG Working Paper Series 145, Bamberg University, Bamberg Economic Research Group.
    5. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    6. Philipp Mundt & Simone Alfarano & Mishael Milaković, 2022. "Survival and the Ergodicity of Corporate Profitability," Management Science, INFORMS, vol. 68(5), pages 3726-3734, May.
    7. Proaño, Christian R. & Lojak, Benjamin, 2020. "Animal spirits, risk premia and monetary policy at the zero lower bound," Journal of Economic Behavior & Organization, Elsevier, vol. 171(C), pages 221-233.

    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. Martin Carolin & Westerhoff Frank, 2019. "Regulating Speculative Housing Markets via Public Housing Construction Programs: Insights from a Heterogeneous Agent Model," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 239(4), pages 627-660, August.
    2. Hommes, Cars & Lustenhouwer, Joep & Mavromatis, Kostas, 2018. "Fiscal consolidations and heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 173-205.
    3. Hommes, Cars & Lustenhouwer, Joep, 2019. "Managing unanchored, heterogeneous expectations and liquidity traps," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 1-16.
    4. Lustenhouwer, Joep & Mavromatis, Kostas, 2017. "Fiscal consolidations and finite planning horizons," BERG Working Paper Series 130, Bamberg University, Bamberg Economic Research Group.
    5. March, Christoph & Sahm, Marco, 2018. "Contests as selection mechanisms: The impact of risk aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 114-131.
    6. Mundt, Philipp & Oh, Ilfan, 2019. "Asymmetric competition, risk, and return distribution," BERG Working Paper Series 145, Bamberg University, Bamberg Economic Research Group.
    7. Proaño, Christian R. & Lojak, Benjamin, 2020. "Animal spirits, risk premia and monetary policy at the zero lower bound," Journal of Economic Behavior & Organization, Elsevier, vol. 171(C), pages 221-233.
    8. Arata, Yoshiyuki & Mundt, Philipp, 2019. "Topology and formation of production input interlinkages: Evidence from Japanese microdata," BERG Working Paper Series 152, Bamberg University, Bamberg Economic Research Group.
    9. Sahm, Marco, 2017. "Are sequential round-robin tournaments discriminatory?," BERG Working Paper Series 121, Bamberg University, Bamberg Economic Research Group.
    10. Sahm, Marco, 2017. "Risk aversion and prudence in contests," BERG Working Paper Series 120, Bamberg University, Bamberg Economic Research Group.
    11. March, Christoph & Sahm, Marco, 2017. "Asymmetric discouragement in asymmetric contests," Economics Letters, Elsevier, vol. 151(C), pages 23-27.
    12. Dieci, Roberto & Schmitt, Noemi & Westerhoff, Frank, 2018. "Interactions between stock, bond and housing markets," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 43-70.
    13. Christoph March & Marco Sahm, 2019. "The Perks of Being in the Smaller Team: Incentives in Overlapping Contests," CESifo Working Paper Series 7994, CESifo.
    14. Sahm, Marco, 2016. "Advance-purchase financing of projects with few buyers," BERG Working Paper Series 118, Bamberg University, Bamberg Economic Research Group.
    15. Herold, Florian & Kuzmics, Christoph, 2020. "The evolution of taking roles," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 38-63.
    16. González-Díaz, Julio & Herold, Florian & Domínguez, Diego, 2016. "Strategic sequential voting," BERG Working Paper Series 113, Bamberg University, Bamberg Economic Research Group.
    17. Dieci, Roberto & Schmitt, Noemi & Westerhoff, Frank H., 2022. "Boom-bust cycles and asset market participation waves: Momentum, value, risk and herding," BERG Working Paper Series 177, Bamberg University, Bamberg Economic Research Group.
    18. Blaurock, Ivonne & Schmitt, Noemi & Westerhoff, Frank, 2018. "Market entry waves and volatility outbursts in stock markets," Journal of Economic Behavior & Organization, Elsevier, vol. 153(C), pages 19-37.
    19. Lojak, Benjamin, 2016. "Sentiment-driven investment, non-linear corporate debt dynamics and co-existing business cycle regimes," BERG Working Paper Series 112, Bamberg University, Bamberg Economic Research Group.
    20. Noemi Schmitt & Ivonne Schwartz & Frank Westerhoff, 2022. "Heterogeneous speculators and stock market dynamics: a simple agent-based computational model," The European Journal of Finance, Taylor & Francis Journals, vol. 28(13-15), pages 1263-1282, October.

    More about this item

    Keywords

    Multi-asset markets; Replicator dynamics; Nonlinear maps; Stability and bifurcation analysis;
    All these keywords.

    JEL classification:

    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G41 - Financial Economics - - Behavioral Finance - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making in Financial Markets

    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:spr:decfin:v:41:y:2018:i:2:d:10.1007_s10203-018-0214-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.