Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
978990 | Physica A: Statistical Mechanics and its Applications | 2008 | 12 Pages |
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. We are mainly interested in the most probable value xmp of the budget that reaches a constant value over time. Based on an analytical investigation of the dynamics, we are able to predict xmpstat. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Jesús Emeterio Navarro-Barrientos, Rubén Cantero-Álvarez, João F. Matias Rodrigues, Frank Schweitzer,