IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0709.3630.html
   My bibliography  Save this paper

Investments in Random Environments

Author

Listed:
  • Emeterio Navarro
  • Ruben Cantero
  • Joao Rodrigues
  • Frank Schweitzer

Abstract

We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on investment, $r(t)$, for which different model assumptions are discussed. The fat-tail distribution of the budget is investigated and compared with theoretical predictions. Weare mainly interested in the most probable value $x_mp$ of the budget that reaches a constant value over time. Based on an analytical investigation of the dynamics, we are able to predict $x_mp^stat$. We find a scaling law that relates the most probable value to the characteristic parameters describing the stochastic process. Our analytical results are confirmed by stochastic computer simulations that show a very good agreement with the predictions.

Suggested Citation

  • Emeterio Navarro & Ruben Cantero & Joao Rodrigues & Frank Schweitzer, 2007. "Investments in Random Environments," Papers 0709.3630, arXiv.org, revised Sep 2008.
    • Handle: RePEc:arx:papers:0709.3630
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0709.3630
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    2. Matteo Richiardi, 2004. "Generalizing Gibrat: Reasonable Multiplicative Models of Firm Dynamics," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 7(1), pages 1-2.
    3. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
    4. J. Emeterio Navarro-Barrientos & Frank E. Walter & Frank Schweitzer, 2008. "Risk-Seeking Versus Risk-Avoiding Investments In Noisy Periodic Environments," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 971-994.
    5. Blank, Aharon & Solomon, Sorin, 2000. "Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 279-288.
    6. Ofer Malcai & Ofer Biham & Peter Richmond & Sorin Solomon, 2002. "Theoretical Analysis and Simulations of the Generalized Lotka-Volterra Model," Papers cond-mat/0208514, arXiv.org.
    7. Navarro-Barrientos, Jesús Emeterio & Cantero-Álvarez, Rubén & Matias Rodrigues, João F. & Schweitzer, Frank, 2008. "Investments in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2035-2046.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Parkes, David C. & Huberman, Bernardo A., 2001. "Multiagent Cooperative Search for Portfolio Selection," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 124-165, April.
    10. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    11. Gode, Dhananjay K & Sunder, Shyam, 1993. "Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 119-137, February.
    12. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 255-272, October.
    13. Hiroshi Takahashi & Takao Terano, 2003. "Agent-Based Approach to Investors? Behavior and Asset Price Fluctuation in Financial Markets," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 6(3), pages 1-3.
    14. J. Doyne Farmer & Paolo Patelli & Ilija I. Zovko, 2003. "The Predictive Power of Zero Intelligence in Financial Markets," Papers cond-mat/0309233, arXiv.org, revised Feb 2004.
    15. Carpenter, Jeffrey P, 2002. "Evolutionary Models of Bargaining: Comparing Agent-Based Computational and Analytical Approaches to Understanding Convention Evolution," Computational Economics, Springer;Society for Computational Economics, vol. 19(1), pages 25-49, February.
    16. Sorin Solomon & Peter Richmond, 2000. "Stability of Pareto-Zipf Law in Non-Stationary Economies," Papers cond-mat/0012479, arXiv.org, revised Jan 2001.
    17. Markowitz, Harry M, 1991. "Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
    18. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    19. LeBaron, Blake, 2000. "Agent-based computational finance: Suggested readings and early research," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 679-702, June.
    20. Thomas Lux & Michele Marchesi, 2000. "Volatility Clustering In Financial Markets: A Microsimulation Of Interacting Agents," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 675-702.
    21. C. Lawrenz & F. Westerhoff, 2003. "Modeling Exchange Rate Behavior with a Genetic Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 209-229, June.
    22. P. Richmond, 2001. "Power law distributions and dynamic behaviour of stock markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 523-526, April.
    23. Sergei Maslov & Yi-Cheng Zhang, 1998. "Optimal Investment Strategy for Risky Assets," Papers cond-mat/9801240, arXiv.org.
    24. Klos, Tomas B. & Nooteboom, Bart, 2001. "Agent-based computational transaction cost economics," Journal of Economic Dynamics and Control, Elsevier, vol. 25(3-4), pages 503-526, March.
    25. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
    26. Peter Richmond & Sorin Solomon, 2001. "Power Laws Are Disguised Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 333-343.
    27. Moshe Levy & Sorin Solomon, 1996. "Power Laws Are Logarithmic Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 595-601.
    28. Aoyama, Hideaki & Fujiwara, Yoshi & Souma, Wataru, 2004. "Kinematics and dynamics of Pareto–Zipf's law and Gibrat's law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 117-121.
    29. Bera, Anil K & Higgins, Matthew L, 1993. "ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
    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. J. Emeterio Navarro-Barrientos & Frank E. Walter & Frank Schweitzer, 2008. "Risk-Seeking Versus Risk-Avoiding Investments In Noisy Periodic Environments," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 971-994.
    2. Navarro-Barrientos, Jesús Emeterio & Cantero-Álvarez, Rubén & Matias Rodrigues, João F. & Schweitzer, Frank, 2008. "Investments in random environments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2035-2046.

    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. J. Emeterio Navarro-Barrientos & Frank E. Walter & Frank Schweitzer, 2008. "Risk-Seeking Versus Risk-Avoiding Investments In Noisy Periodic Environments," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 971-994.
    2. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    3. Arvid Oskar Ivar Hoffmann & Wander Jager & J. H. Von Eije, 2007. "Social Simulation of Stock Markets: Taking It to the Next Level," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(2), pages 1-7.
    4. Segarra, Agustí & Teruel, Mercedes, 2012. "An appraisal of firm size distribution: Does sample size matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 314-328.
    5. McMillan, David G. & Speight, Alan E. H., 2001. "Non-ferrous metals price volatility: a component analysis," Resources Policy, Elsevier, vol. 27(3), pages 199-207, September.
    6. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2001. "Microscopic Models of Financial Markets," Papers cond-mat/0110354, arXiv.org.
    7. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    8. David McMillan & Alan Speight, 2006. "Heterogeneous information flows and intra-day volatility dynamics: evidence from the UK FTSE-100 stock index futures market," Applied Financial Economics, Taylor & Francis Journals, vol. 16(13), pages 959-972.
    9. 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.
    10. Tubbenhauer, Tobias & Fieberg, Christian & Poddig, Thorsten, 2021. "Multi-agent-based VaR forecasting," Journal of Economic Dynamics and Control, Elsevier, vol. 131(C).
    11. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    12. Johann Lussange & Ivan Lazarevich & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2021. "Modelling Stock Markets by Multi-agent Reinforcement Learning," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 113-147, January.
    13. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    14. Black, Angela J. & McMillan, David G., 2006. "Asymmetric risk premium in value and growth stocks," International Review of Financial Analysis, Elsevier, vol. 15(3), pages 237-246.
    15. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
    16. Hong, Yongmiao, 2001. "A test for volatility spillover with application to exchange rates," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 183-224, July.
    17. David Rushing Dewhurst & Michael Vincent Arnold & Colin Michael Van Oort, 2018. "Selection mechanisms affect volatility in evolving markets," Papers 1812.05657, arXiv.org, revised Apr 2019.
    18. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. J. Doyne Farmer & John Geanakoplos, 2008. "The virtues and vices of equilibrium and the future of financial economics," Papers 0803.2996, arXiv.org.
    20. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.

    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:0709.3630. 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.