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A quantitative description for efficient financial markets

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  • Immonen, Eero

Abstract

In this article we develop a control system model for describing efficient financial markets. We define the efficiency of a financial market in quantitative terms by robust asymptotic price–value equality in this model. By invoking the Internal Model Principle of robust output regulation theory we then show that under No Bubble Conditions, in the proposed model, the market is efficient if and only if the following conditions hold true: (1) the traders, as a group, can identify any mispricing in asset value (even if no one single trader can do it accurately), and (2) the traders, as a group, incorporate an internal model of the value process (again, even if no one single trader knows it). This main result of the article, which deliberately avoids the requirement for investor rationality, demonstrates, in quantitative terms, that the more transparent the markets are, the more efficient they are. An extensive example is provided to illustrate the theoretical development.

Suggested Citation

  • Immonen, Eero, 2015. "A quantitative description for efficient financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 171-181.
    • Handle: RePEc:eee:phsmap:v:433:y:2015:i:c:p:171-181
    DOI: 10.1016/j.physa.2015.03.032
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    References listed on IDEAS

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    1. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
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    6. Schulmeister, Stephan, 2009. "Profitability of technical stock trading: Has it moved from daily to intraday data?," Review of Financial Economics, Elsevier, vol. 18(4), pages 190-201, October.
    7. Walker, Donald A, 1987. "Walras's Theories of Tatonnement," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 758-774, August.
    8. Alvarez-Ramirez, Jose & Suarez, Rodolfo & Ibarra-Valdez, Carlos, 2003. "Trading strategies, feedback control and market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 220-226.
    9. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
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    Cited by:

    1. Ivani Mausumi Bora & Manoj Kumar, 2017. "Long Term Dynamics of Indian ADRs Market: The Case of Persistence and Irregular Cycles," Accounting and Finance Research, Sciedu Press, vol. 6(2), pages 1-71, May.
    2. Damian Pastor & Pavel Kisela & Viliam Kovac & Tomas Sabol & Viliam Vajda, 2015. "Application Of Market Valuation Models In Portfolio Management," Polish Journal of Management Studies, Czestochowa Technical University, Department of Management, vol. 12(1), pages 154-165, DEcember.
    3. Rounaghi, Mohammad Mahdi & Nassir Zadeh, Farzaneh, 2016. "Investigation of market efficiency and Financial Stability between S&P 500 and London Stock Exchange: Monthly and yearly Forecasting of Time Series Stock Returns using ARMA model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 10-21.
    4. Meng, Xiangyi & Zhang, Jian-Wei & Guo, Hong, 2016. "Quantum Brownian motion model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 281-288.
    5. Immonen, Eero, 2017. "Simple agent-based dynamical system models for efficient financial markets: Theory and examples," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 38-53.

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