Economy – Quantitative Finance – Portfolio Management
Scientific paper
2007-09-23
Physica A, vol. 387, no. 8-9 (2008), pp. 2035-2046
Economy
Quantitative Finance
Portfolio Management
19 pp., corrections and extensions to compare with other approaches
Scientific paper
10.1016/j.physa.2007.11.029
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.
Cantero Ruben
Navarro Emeterio
Rodrigues José J.
Schweitzer Frank
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