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Investments in Random Environments

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Author Info
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.

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File URL: http://arxiv.org/abs/0709.3630
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0709.3630.

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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
Handle: RePEc:arx:papers:0709.3630

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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.:
  1. Markowitz, Harry M, 1991. " Foundations of Portfolio Theory," Journal of Finance, American Finance Association, vol. 46(2), pages 469-77, June. [Downloadable!] (restricted)
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  2. Carpenter, Jeffrey P, 2002. "Evolutionary Models of Bargaining: Comparing Agent-Based Computational and Analytical Approaches to Understanding Convention Evolution," Computational Economics, Springer, vol. 19(1), pages 25-49, February. [Downloadable!]
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  4. Sorin Solomon & Peter Richmond, 2000. "Stability of Pareto-Zipf Law in Non-Stationary Economies," Quantitative Finance Papers cond-mat/0012479, arXiv.org, revised Jan 2001. [Downloadable!]
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  6. 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. [Downloadable!]
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  7. Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003. "Traders' Long-Run Wealth in an Artificial Financial Market," Computational Economics, Springer, vol. 22(2), pages 255-272, October. [Downloadable!] (restricted)
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  8. 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 119-37, February. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. C. Lawrenz & F. Westerhoff, 2003. "Modeling Exchange Rate Behavior with a Genetic Algorithm," Computational Economics, Springer, vol. 21(3), pages 209-229, June. [Downloadable!] (restricted)
  11. Ofer Malcai & Ofer Biham & Peter Richmond & Sorin Solomon, 2002. "Theoretical Analysis and Simulations of the Generalized Lotka-Volterra Model," Quantitative Finance Papers cond-mat/0208514, arXiv.org. [Downloadable!]
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  1. J. Emeterio Navarro Barrientos & Frank E. Walter & Frank Schweitzer, 2008. "Risk-Seeking versus Risk-Avoiding Investments in Noisy Periodic Environments," Quantitative Finance Papers 0801.4305, arXiv.org, revised Sep 2008. [Downloadable!]
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