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Entropy corrected geometric Brownian motion

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Listed:
  • Rishabh Gupta
  • Ewa A. Drzazga-Szczc{e}'sniak
  • Sabre Kais
  • Dominik Szczc{e}'sniak

Abstract

The geometric Brownian motion (GBM) is widely employed for modeling stochastic processes, yet its solutions are characterized by the log-normal distribution. This comprises predictive capabilities of GBM mainly in terms of forecasting applications. Here, entropy corrections to GBM are proposed to go beyond log-normality restrictions and better account for intricacies of real systems. It is shown that GBM solutions can be effectively refined by arguing that entropy is reduced when deterministic content of considered data increases. Notable improvements over conventional GBM are observed for several cases of non-log-normal distributions, ranging from a dice roll experiment to real world data.

Suggested Citation

  • Rishabh Gupta & Ewa A. Drzazga-Szczc{e}'sniak & Sabre Kais & Dominik Szczc{e}'sniak, 2024. "Entropy corrected geometric Brownian motion," Papers 2403.06253, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2403.06253
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