Entropy corrected geometric Brownian motion
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911799038705664 |
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| author | Gupta, Rishabh Drzazga-Szczȩśniak, Ewa A. Kais, Sabre Szczȩśniak, Dominik |
| author_facet | Gupta, Rishabh Drzazga-Szczȩśniak, Ewa A. Kais, Sabre Szczȩśniak, Dominik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06253 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropy corrected geometric Brownian motion Gupta, Rishabh Drzazga-Szczȩśniak, Ewa A. Kais, Sabre Szczȩśniak, Dominik Data Analysis, Statistics and Probability Statistical Finance 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. |
| title | Entropy corrected geometric Brownian motion |
| topic | Data Analysis, Statistics and Probability Statistical Finance |
| url | https://arxiv.org/abs/2403.06253 |