Investments in Random Environments
arXiv:0709.3630 · doi:10.1016/j.physa.2007.11.029
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, , depends on the stochasticity of the return on investment, , 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 of the budget that reaches a constant value over time. Based on an analytical investigation of the dynamics, we are able to predict . 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.
19 pp., corrections and extensions to compare with other approaches
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