IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1912.09679.html
   My bibliography  Save this paper

From Disequilibrium Markets to Equilibrium

Author

Listed:
  • Christian Lax
  • Torsten Trimborn

Abstract

The modeling of financial markets as disequilibrium models by ordinary differential equations has become a popular modeling tool. One famous example of such a model is the Beja-Goldman model(The Journal of Finance, 1980) which we consider in this paper. We study the passage from disequilibrium dynamics to equilibrium. Mathematically, this limit corresponds to an asymptotic limit also known as a Tikhonov-Fenichel reduction. Furthermore, we analyze the stability of the reduced equilibrium model and discuss the economic implications. We conduct several numerical examples to visualize and support our analysis.

Suggested Citation

  • Christian Lax & Torsten Trimborn, 2019. "From Disequilibrium Markets to Equilibrium," Papers 1912.09679, arXiv.org.
    • Handle: RePEc:arx:papers:1912.09679
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1912.09679
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    2. Day, Richard H. & Huang, Weihong, 1990. "Bulls, bears and market sheep," Journal of Economic Behavior & Organization, Elsevier, vol. 14(3), pages 299-329, December.
    3. Carl Chiarella, 1992. "Developments in Nonlinear Economic Dynamics: Past, Present and Future," Working Paper Series 14, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2011. "The dynamic behaviour of asset prices in disequilibrium: a survey," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 101-139.
    5. Mantel, Rolf R., 1974. "On the characterization of aggregate excess demand," Journal of Economic Theory, Elsevier, vol. 7(3), pages 348-353, March.
    6. Avraham Beja and Nils H. Hakansson., 1977. "From Orders to Trades: Some Alternative Market Mechanisms," Research Program in Finance Working Papers 56, University of California at Berkeley.
    7. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    8. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    9. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    10. Kempf, Alexander & Korn, Olaf, 1999. "Market depth and order size1," Journal of Financial Markets, Elsevier, vol. 2(1), pages 29-48, February.
    11. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2006. "Asset price and wealth dynamics in a financial market with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1755-1786.
    12. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    13. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    14. Franke, Reiner & Westerhoff, Frank, 2012. "Structural stochastic volatility in asset pricing dynamics: Estimation and model contest," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1193-1211.
    15. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    16. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(2), pages 170-196, June.
    17. Beja, Avraham & Goldman, M Barry, 1980. "On the Dynamic Behavior of Prices in Disequilibrium," Journal of Finance, American Finance Association, vol. 35(2), pages 235-248, May.
    18. Sonnenschein, Hugo, 1972. "Market Excess Demand Functions," Econometrica, Econometric Society, vol. 40(3), pages 549-563, May.
    19. Levy, Haim & Levy, Moshe & Solomon, Sorin, 2000. "Microscopic Simulation of Financial Markets," Elsevier Monographs, Elsevier, edition 1, number 9780124458901.
    20. Chiarella, Carl, 1986. "Perfect foresight models and the dynamic instability problem from a higher viewpoint," Economic Modelling, Elsevier, vol. 3(4), pages 283-292, October.
    21. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    22. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    23. Carl Chiarella, 1992. "The Dynamics of Speculative Behaviour," Working Paper Series 13, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    24. Frankel, Jeffrey A & Froot, Kenneth A, 1990. "Chartists, Fundamentalists, and Trading in the Foreign Exchange Market," American Economic Review, American Economic Association, vol. 80(2), pages 181-185, May.
    25. Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
    26. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    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. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2020. "Robust Mathematical Formulation And Probabilistic Description Of Agent-Based Computational Economic Market Models," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-41, September.

    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. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    2. Torsten Trimborn & Philipp Otte & Simon Cramer & Max Beikirch & Emma Pabich & Martin Frank, 2018. "SABCEMM-A Simulator for Agent-Based Computational Economic Market Models," Papers 1801.01811, arXiv.org, revised Oct 2018.
    3. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2011. "The dynamic behaviour of asset prices in disequilibrium: a survey," International Journal of Behavioural Accounting and Finance, Inderscience Enterprises Ltd, vol. 2(2), pages 101-139.
    4. Carl Chiarella & Roberto Dieci & Xue-Zhong He, 2008. "Heterogeneity, Market Mechanisms, and Asset Price Dynamics," Research Paper Series 231, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2014.
    6. Kai Li, 2014. "Asset Price Dynamics with Heterogeneous Beliefs and Time Delays," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 13, July-Dece.
    7. 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.
    8. 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.
    9. 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.
    10. Qi Nan Zhai, 2015. "Asset Pricing Under Ambiguity and Heterogeneity," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2015.
    11. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    12. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    13. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    14. Simon Cramer & Torsten Trimborn, 2019. "Stylized Facts and Agent-Based Modeling," Papers 1912.02684, arXiv.org.
    15. Qi Nan Zhai, 2015. "Asset Pricing Under Ambiguity and Heterogeneity," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 16, July-Dece.
    16. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2006. "Asset price and wealth dynamics in a financial market with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1755-1786.
    17. Hommes, C.H., 2005. "Heterogeneous Agent Models in Economics and Finance, In: Handbook of Computational Economics II: Agent-Based Computational Economics, edited by Leigh Tesfatsion and Ken Judd , Elsevier, Amsterdam 2006," CeNDEF Working Papers 05-03, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    18. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    19. Zhu, Mei & Chiarella, Carl & He, Xue-Zhong & Wang, Duo, 2009. "Does the market maker stabilize the market?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3164-3180.
    20. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2019. "Robust Mathematical Formulation and Probabilistic Description of Agent-Based Computational Economic Market Models," Papers 1904.04951, arXiv.org, revised Mar 2021.

    More about this item

    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:arx:papers:1912.09679. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.