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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
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    References listed on IDEAS

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    1. repec:wsi:ijmpcx:v:19:y:2008:i:06:n:s0129183108012662 is not listed on IDEAS
    2. 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.
    3. 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.

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