Figure 1.
Manuscript statistics from 2020 to 2022.
Anomalous diffusion (AD) describes transport phenomena where the mean-square displacement (MSD) of a particle does not scale linearly with time, deviating from classical diffusion. This behavior, often linked to non-equilibrium phenomena, sheds light on the underlying mechanisms in various systems, including biological and financial domains.
Integrating insights from anomalous diffusion into financial analysis could significantly improve our understanding of market behaviors, similar to their impacts on biological systems. In financial markets, accurately estimating asset volatility—whether historical or implied—is vital for investors.
We introduce a novel methodology to estimate the volatility of stocks and similar assets, combining anomalous diffusion principles with machine learning. Our architecture combines convolutional and recurrent neural networks (bidirectional long short-term memory units). Our model computes the diffusion exponent of a financial time series to measure its volatility and it categorizes market movements into five diffusion models: annealed transit time motion (ATTM), continuous time random walk (CTRW), fractional Brownian motion (FBM), Lévy walk (LW), and scaled Brownian motion (SBM).
Our findings suggest that the diffusion exponent derived from anomalous diffusion processes provides insightful and novel perspectives on stock market volatility. By differentiating between subdiffusion, superdiffusion, and normal diffusion, our methodology offers a more nuanced understanding of market dynamics than traditional volatility metrics.
Citation: Rubén V. Arévalo, J. Alberto Conejero, Òscar Garibo-i-Orts, Alfred Peris. Stock volatility as an anomalous diffusion process[J]. AIMS Mathematics, 2024, 9(12): 34947-34965. doi: 10.3934/math.20241663
| [1] | Kelly Pagidas . 2024 Annual Report. AIMS Medical Science, 2025, 12(1): 63-68. doi: 10.3934/medsci.2025005 |
| [2] | Ragini C Bhake, Stafford L Lightman . A Simple Complex Case: Restoration of Circadian Cortisol Activity. AIMS Medical Science, 2015, 2(3): 182-185. doi: 10.3934/medsci.2015.3.182 |
| [3] | Mpumelelo Nyathi, Autherlia Dimpho Rinkie Mosiame . Evaluating radiation exposure risks from patient urine in a PET-CT center: should concerns arise?. AIMS Medical Science, 2025, 12(2): 238-246. doi: 10.3934/medsci.2025016 |
| [4] | Piero Pavone, Ottavia Avola, Claudia Oliva, Alessandra Di Nora, Tiziana Timpanaro, Chiara Nannola, Filippo Greco, Raffaele Falsaperla, Agata Polizzi . Genetic epilepsy and role of mutation variants in 27 epileptic children: results from a “single tertiary centre” and literature review. AIMS Medical Science, 2024, 11(3): 330-347. doi: 10.3934/medsci.2024023 |
| [5] | Muhammad Bilal . Leukemoid reaction in paraplegic male with pressure injuries: A case report. AIMS Medical Science, 2024, 11(2): 72-76. doi: 10.3934/medsci.2024006 |
| [6] | Niccolò Stomeo, Giacomo Simeone, Leonardo Ciavarella, Giulia Lionetti, Arosh S. Perera Molligoda Arachchige, Francesco Cama . Fluid overload during operative hysteroscopy for metroplasty: A case report. AIMS Medical Science, 2023, 10(4): 310-317. doi: 10.3934/medsci.2023024 |
| [7] | Ryan T. Borne, Arash Aghel, Amit C. Patel, Robert K. Rogers . Innominate Steal Syndrome: A Two Patient Case Report and Review. AIMS Medical Science, 2015, 2(4): 360-370. doi: 10.3934/medsci.2015.4.360 |
| [8] | Rosario Megna . Evolution of the COVID-19 pandemic in Italy at the national and regional levels from February 2020 to March 2022. AIMS Medical Science, 2023, 10(3): 237-258. doi: 10.3934/medsci.2023019 |
| [9] | Juliet A Harvey, Sebastien FM Chastin, Dawn A Skelton . What happened to my legs when I broke my arm?. AIMS Medical Science, 2018, 5(3): 252-258. doi: 10.3934/medsci.2018.3.252 |
| [10] | Jamie L. Flexon, Lisa Stolzenberg, Stewart J. D'Alessio . The effect of cannabis legislation on opioid and benzodiazepine use among aging Americans. AIMS Medical Science, 2024, 11(4): 361-377. doi: 10.3934/medsci.2024025 |
Anomalous diffusion (AD) describes transport phenomena where the mean-square displacement (MSD) of a particle does not scale linearly with time, deviating from classical diffusion. This behavior, often linked to non-equilibrium phenomena, sheds light on the underlying mechanisms in various systems, including biological and financial domains.
Integrating insights from anomalous diffusion into financial analysis could significantly improve our understanding of market behaviors, similar to their impacts on biological systems. In financial markets, accurately estimating asset volatility—whether historical or implied—is vital for investors.
We introduce a novel methodology to estimate the volatility of stocks and similar assets, combining anomalous diffusion principles with machine learning. Our architecture combines convolutional and recurrent neural networks (bidirectional long short-term memory units). Our model computes the diffusion exponent of a financial time series to measure its volatility and it categorizes market movements into five diffusion models: annealed transit time motion (ATTM), continuous time random walk (CTRW), fractional Brownian motion (FBM), Lévy walk (LW), and scaled Brownian motion (SBM).
Our findings suggest that the diffusion exponent derived from anomalous diffusion processes provides insightful and novel perspectives on stock market volatility. By differentiating between subdiffusion, superdiffusion, and normal diffusion, our methodology offers a more nuanced understanding of market dynamics than traditional volatility metrics.
It is with admiration that we share with you our publication data for the 2022 calendar year for the AIMS Medical Science Journal. It was another successful year with the highest number of publication submissions to date over the past three years. Our depth and breadth of publications spanned multiple basic and clinical science disciplines that originated from talented authors across the globe. We look forward to an exciting year ahead and welcome the opportunity to review original manuscripts for consideration for publication in the journal. Our goals are to provide a forum of high-quality manuscripts that can positively impact the expansion of scientific knowledge and advance the health of our population.
Below is a graphic depiction of the manuscript submission and publication data for the journal for the past three years (Figure 1). There are slightly more submissions that were received in 2022 than in 2021, and the number of accepted and published manuscripts remain stable for the past three years. Our hope is increasing the footprint of quality manuscripts submitted to the journal that will translate into an increased number of high-quality publications for the upcoming year.
2022 manuscripts status:
Publications: 28
Reject rate: 71%
Publication time (from submission to online): 109 days
The geographic distribution of the corresponding authors of the published manuscripts are depicted below (Figure 2). We are honored to attract authors from around the world who chose to submit their research to the journal for publication (USA, Canada, Nigeria, Japan, etc.). Of note the majority of publications originate from authors based in the United States representing 39% of the publications followed by Canada and Nigeria standing at 11% each.
Table 1 depicts the type of manuscripts published. A total of 28 articles were published in 2022, of which, the majority were research based, 12 (43%) followed by reviews, 10 (36%).
| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
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Table 2 depicts the top 10 articles with the highest views, published in 2022. A focus of these top 10 articles was: Fall Risks, Monoclonal Antibody development and COVID-19.
| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
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AIMS Medical Science Journal has 94 members, representing 26 countries. Thirty three percent of the members are from the United States, and other members represent Italy, France, and several other countries (Figure 3). We want to particularly acknowledge our editors: Kelly Pagidas (Editor-in-Chief), Belgüzar Kara, Gulshan Sunavala-Dossabhoy, Gwendolyn Quinn, Panayota Mitrou, Kimberly Udlis (retired), Mai Alzamel, Yi-Jang Lee, Sreekumar Othumpangat, Ji Hyun Kim, Athanasios Alexiou, Robert Striker, Andrei Kelarev, Casey Peiris, Patrick Legembre, Ramin Ataee, Louis Ragolia, Bogdan Borz, Robert Kratzke, Maria Fiorillo, Lars Malmström, Giuliana Banche, Jean-Marie Exbrayat and Elias El-Habr. Importantly, a special thank you to all the Editorial Board members, reviewers and in-house editors, and staff for their dedication, commitment, and unrelenting hard work throughout the year. We hope to attract additional scholars that will be able to join our team for the upcoming year.
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Figures(3) / Tables(4)
Rubén V. Arévalo, J. Alberto Conejero, Òscar Garibo-i-Orts, Alfred Peris. Stock volatility as an anomalous diffusion process[J]. AIMS Mathematics, 2024, 9(12): 34947-34965. doi: 10.3934/math.20241663
| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
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| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
DownLoad:
CSV
| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
