Investments in Random Environments
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.
|Date of creation:||Sep 2007|
|Date of revision:||Sep 2008|
|Publication status:||Published in Physica A, vol. 387, no. 8-9 (2008), pp. 2035-2046|
|Contact details of provider:|| Web page: http://arxiv.org/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Lux, T. & M. Marchesi, "undated". "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
- 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.
- 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.
- 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.
- 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.
- 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.
- Matteo Richiardi, 2003. "Generalizing Gibrat. Reasonable Multiplicative Models of Firm Dynamics," Industrial Organization 0304004, EconWPA.
- Sorin Solomon & Peter Richmond, 2000. "Stability of Pareto-Zipf Law in Non-Stationary Economies," Papers cond-mat/0012479, arXiv.org, revised Jan 2001.
- Sorin Solomon and Peter Richmond, 2001. "Stability of Pareto-Zipf Law in Non-Stationary Economies," Computing in Economics and Finance 2001 11, Society for Computational Economics.
- John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
- 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.
- 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.
- Marco Raberto & Silvano Cincott & Sergio M. Focardi & Michele Marchesi, 2002. "Traders’ long-run wealth in an artificial financial market," Computing in Economics and Finance 2002 301, Society for Computational Economics.
- 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.
- 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.
- 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.
- 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.
- Emeterio Navarro & Ruben Cantero & Joao Rodrigues & Frank Schweitzer, 2007. "Investments in Random Environments," Papers 0709.3630, arXiv.org, revised Sep 2008.
- Markowitz, Harry M, 1991. " Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-477, June.
- Markowitz, Harry M., 1990. "Foundations of Portfolio Theory," Nobel Prize in Economics documents 1990-1, Nobel Prize Committee.
- 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.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Sergei Maslov & Yi-Cheng Zhang, 1998. "Optimal Investment Strategy for Risky Assets," Papers cond-mat/9801240, arXiv.org.
- 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.
- 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.
- 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.
- Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
- J. Emeterio Navarro Barrientos & Frank E. Walter & Frank Schweitzer, 2008. "Risk-Seeking versus Risk-Avoiding Investments in Noisy Periodic Environments," Papers 0801.4305, arXiv.org, revised Sep 2008.
- Sorin Solomon & Peter Richmond, 2001. "Power Laws of Wealth, Market Order Volumes and Market Returns," Papers cond-mat/0102423, arXiv.org, revised Apr 2001.
- 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.
- 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. Full references (including those not matched with items on IDEAS)