A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation

Coulibaly Bakary D; Badiane Marcel Sihintoe; Kalivogui Siba; Ghizlane Chaibi

doi:doi:10.11648/j.ajist.20250902.15

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| Peer-Reviewed

A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation

Coulibaly Bakary D^*

, Badiane Marcel Sihintoe

, Kalivogui Siba

, Ghizlane Chaibi

Published in American Journal of Information Science and Technology (Volume 9, Issue 2)

Received: 23 March 2025 Accepted: 1 April 2025 Published: 3 June 2025

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Abstract

This study examines portfolio risk assessment in finance using advanced quantile and superquantile techniques. The portfolio analyzed consists of widely recognized stocks, including Apple (AAPL), Microsoft (MSFT), Alphabet (GOOGL), and Tesla (TSLA). The primary objective is to enhance the accuracy and robustness of financial risk evaluation for such a portfolio. To achieve this, we developed innovative methods for computing quantiles and superquantiles, leveraging various probability distributions. In particular, we explored the Exponential, Gumbel, Frchet, and α-stable distributions to model the returns of the selected equities. The parameters of these distributions were estimated based on historical financial data over a defined time horizon. By doing so, we aimed to better capture the statistical characteristics of asset returns and their tail behavior, which is crucial for effective risk management. The findings reveal that these advanced quantile and superquantile approaches provide deeper insights into the potential risks associated with the portfolio. Compared to traditional risk metrics, such as Value at Risk (VaR) and Expected Shortfall (ES), the proposed methodologies offer a more refined evaluation of extreme losses and downside risks. Additionally, the study highlights how different distributional assumptions impact risk estimates, demonstrating the importance of selecting appropriate models for financial data analysis. Furthermore, we illustrate how these improved risk assessment techniques can assist investors and portfolio managers in making more informed decisions regarding risk exposure. By integrating these methods into risk management frameworks, financial professionals can enhance their ability to anticipate and mitigate adverse market conditions. Ultimately, this research contributes to the ongoing efforts to refine quantitative finance tools, ensuring more reliable and data-driven decision-making in portfolio management.

Published in	American Journal of Information Science and Technology (Volume 9, Issue 2)
DOI	10.11648/j.ajist.20250902.15
Page(s)	111-127
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Superquantil, Quantile, Portfolio Risk Assessment, Density Estimation, Financial, Probability Distributions, Portfolio Optimization, Stable Distribution

References

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APA Style

D, C. B., Sihintoe, B. M., Siba, K., Chaibi, G. (2025). A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation. American Journal of Information Science and Technology, 9(2), 111-127. https://doi.org/10.11648/j.ajist.20250902.15

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ACS Style

D, C. B.; Sihintoe, B. M.; Siba, K.; Chaibi, G. A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation. Am. J. Inf. Sci. Technol. 2025, 9(2), 111-127. doi: 10.11648/j.ajist.20250902.15

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AMA Style

D CB, Sihintoe BM, Siba K, Chaibi G. A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation. Am J Inf Sci Technol. 2025;9(2):111-127. doi: 10.11648/j.ajist.20250902.15

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@article{10.11648/j.ajist.20250902.15,
  author = {Coulibaly Bakary D and Badiane Marcel Sihintoe and Kalivogui Siba and Ghizlane Chaibi},
  title = {A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation},
  journal = {American Journal of Information Science and Technology},
  volume = {9},
  number = {2},
  pages = {111-127},
  doi = {10.11648/j.ajist.20250902.15},
  url = {https://doi.org/10.11648/j.ajist.20250902.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajist.20250902.15},
  abstract = {This study examines portfolio risk assessment in finance using advanced quantile and superquantile techniques. The portfolio analyzed consists of widely recognized stocks, including Apple (AAPL), Microsoft (MSFT), Alphabet (GOOGL), and Tesla (TSLA). The primary objective is to enhance the accuracy and robustness of financial risk evaluation for such a portfolio. To achieve this, we developed innovative methods for computing quantiles and superquantiles, leveraging various probability distributions. In particular, we explored the Exponential, Gumbel, Frchet, and α-stable distributions to model the returns of the selected equities. The parameters of these distributions were estimated based on historical financial data over a defined time horizon. By doing so, we aimed to better capture the statistical characteristics of asset returns and their tail behavior, which is crucial for effective risk management. The findings reveal that these advanced quantile and superquantile approaches provide deeper insights into the potential risks associated with the portfolio. Compared to traditional risk metrics, such as Value at Risk (VaR) and Expected Shortfall (ES), the proposed methodologies offer a more refined evaluation of extreme losses and downside risks. Additionally, the study highlights how different distributional assumptions impact risk estimates, demonstrating the importance of selecting appropriate models for financial data analysis. Furthermore, we illustrate how these improved risk assessment techniques can assist investors and portfolio managers in making more informed decisions regarding risk exposure. By integrating these methods into risk management frameworks, financial professionals can enhance their ability to anticipate and mitigate adverse market conditions. Ultimately, this research contributes to the ongoing efforts to refine quantitative finance tools, ensuring more reliable and data-driven decision-making in portfolio management.},
 year = {2025}
}

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TY  - JOUR
T1  - A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation
AU  - Coulibaly Bakary D
AU  - Badiane Marcel Sihintoe
AU  - Kalivogui Siba
AU  - Ghizlane Chaibi
Y1  - 2025/06/03
PY  - 2025
N1  - https://doi.org/10.11648/j.ajist.20250902.15
DO  - 10.11648/j.ajist.20250902.15
T2  - American Journal of Information Science and Technology
JF  - American Journal of Information Science and Technology
JO  - American Journal of Information Science and Technology
SP  - 111
EP  - 127
PB  - Science Publishing Group
SN  - 2640-0588
UR  - https://doi.org/10.11648/j.ajist.20250902.15
AB  - This study examines portfolio risk assessment in finance using advanced quantile and superquantile techniques. The portfolio analyzed consists of widely recognized stocks, including Apple (AAPL), Microsoft (MSFT), Alphabet (GOOGL), and Tesla (TSLA). The primary objective is to enhance the accuracy and robustness of financial risk evaluation for such a portfolio. To achieve this, we developed innovative methods for computing quantiles and superquantiles, leveraging various probability distributions. In particular, we explored the Exponential, Gumbel, Frchet, and α-stable distributions to model the returns of the selected equities. The parameters of these distributions were estimated based on historical financial data over a defined time horizon. By doing so, we aimed to better capture the statistical characteristics of asset returns and their tail behavior, which is crucial for effective risk management. The findings reveal that these advanced quantile and superquantile approaches provide deeper insights into the potential risks associated with the portfolio. Compared to traditional risk metrics, such as Value at Risk (VaR) and Expected Shortfall (ES), the proposed methodologies offer a more refined evaluation of extreme losses and downside risks. Additionally, the study highlights how different distributional assumptions impact risk estimates, demonstrating the importance of selecting appropriate models for financial data analysis. Furthermore, we illustrate how these improved risk assessment techniques can assist investors and portfolio managers in making more informed decisions regarding risk exposure. By integrating these methods into risk management frameworks, financial professionals can enhance their ability to anticipate and mitigate adverse market conditions. Ultimately, this research contributes to the ongoing efforts to refine quantitative finance tools, ensuring more reliable and data-driven decision-making in portfolio management.
VL  - 9
IS  - 2
ER  -

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Author Information

Coulibaly Bakary D

Department Mathematics, Kindia University Faculty of Sciences, Kindia, Guinea

Contact Email

http://orcid.org/0000-0002-7711-2970
Badiane Marcel Sihintoe

Department Mathematics, Kindia University Faculty of Sciences, Kindia, Guinea

Contact Email

http://orcid.org/0009-0009-6675-8846
Kalivogui Siba

Department Mathematics, Kindia University Faculty of Sciences, Kindia, Guinea

Contact Email

http://orcid.org/0009-0002-8292-1905
Ghizlane Chaibi

Department Mathematics, Sidi Mohamed Ben Abdellah University Faculty of Sciences and Technology, Fez Meknez, Morocco

Contact Email

http://orcid.org/0000-0001-8393-1860

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APA Style

D, C. B., Sihintoe, B. M., Siba, K., Chaibi, G. (2025). A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation. American Journal of Information Science and Technology, 9(2), 111-127. https://doi.org/10.11648/j.ajist.20250902.15

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ACS Style

D, C. B.; Sihintoe, B. M.; Siba, K.; Chaibi, G. A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation. Am. J. Inf. Sci. Technol. 2025, 9(2), 111-127. doi: 10.11648/j.ajist.20250902.15

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AMA Style

D CB, Sihintoe BM, Siba K, Chaibi G. A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation. Am J Inf Sci Technol. 2025;9(2):111-127. doi: 10.11648/j.ajist.20250902.15

Copy | Download

@article{10.11648/j.ajist.20250902.15,
  author = {Coulibaly Bakary D and Badiane Marcel Sihintoe and Kalivogui Siba and Ghizlane Chaibi},
  title = {A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation},
  journal = {American Journal of Information Science and Technology},
  volume = {9},
  number = {2},
  pages = {111-127},
  doi = {10.11648/j.ajist.20250902.15},
  url = {https://doi.org/10.11648/j.ajist.20250902.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajist.20250902.15},
  abstract = {This study examines portfolio risk assessment in finance using advanced quantile and superquantile techniques. The portfolio analyzed consists of widely recognized stocks, including Apple (AAPL), Microsoft (MSFT), Alphabet (GOOGL), and Tesla (TSLA). The primary objective is to enhance the accuracy and robustness of financial risk evaluation for such a portfolio. To achieve this, we developed innovative methods for computing quantiles and superquantiles, leveraging various probability distributions. In particular, we explored the Exponential, Gumbel, Frchet, and α-stable distributions to model the returns of the selected equities. The parameters of these distributions were estimated based on historical financial data over a defined time horizon. By doing so, we aimed to better capture the statistical characteristics of asset returns and their tail behavior, which is crucial for effective risk management. The findings reveal that these advanced quantile and superquantile approaches provide deeper insights into the potential risks associated with the portfolio. Compared to traditional risk metrics, such as Value at Risk (VaR) and Expected Shortfall (ES), the proposed methodologies offer a more refined evaluation of extreme losses and downside risks. Additionally, the study highlights how different distributional assumptions impact risk estimates, demonstrating the importance of selecting appropriate models for financial data analysis. Furthermore, we illustrate how these improved risk assessment techniques can assist investors and portfolio managers in making more informed decisions regarding risk exposure. By integrating these methods into risk management frameworks, financial professionals can enhance their ability to anticipate and mitigate adverse market conditions. Ultimately, this research contributes to the ongoing efforts to refine quantitative finance tools, ensuring more reliable and data-driven decision-making in portfolio management.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - A Comprehensive Examination of CVaR and bPOE in Common Probability Distributions: Applications in Portfolio Optimization and Density Estimation
AU  - Coulibaly Bakary D
AU  - Badiane Marcel Sihintoe
AU  - Kalivogui Siba
AU  - Ghizlane Chaibi
Y1  - 2025/06/03
PY  - 2025
N1  - https://doi.org/10.11648/j.ajist.20250902.15
DO  - 10.11648/j.ajist.20250902.15
T2  - American Journal of Information Science and Technology
JF  - American Journal of Information Science and Technology
JO  - American Journal of Information Science and Technology
SP  - 111
EP  - 127
PB  - Science Publishing Group
SN  - 2640-0588
UR  - https://doi.org/10.11648/j.ajist.20250902.15
AB  - This study examines portfolio risk assessment in finance using advanced quantile and superquantile techniques. The portfolio analyzed consists of widely recognized stocks, including Apple (AAPL), Microsoft (MSFT), Alphabet (GOOGL), and Tesla (TSLA). The primary objective is to enhance the accuracy and robustness of financial risk evaluation for such a portfolio. To achieve this, we developed innovative methods for computing quantiles and superquantiles, leveraging various probability distributions. In particular, we explored the Exponential, Gumbel, Frchet, and α-stable distributions to model the returns of the selected equities. The parameters of these distributions were estimated based on historical financial data over a defined time horizon. By doing so, we aimed to better capture the statistical characteristics of asset returns and their tail behavior, which is crucial for effective risk management. The findings reveal that these advanced quantile and superquantile approaches provide deeper insights into the potential risks associated with the portfolio. Compared to traditional risk metrics, such as Value at Risk (VaR) and Expected Shortfall (ES), the proposed methodologies offer a more refined evaluation of extreme losses and downside risks. Additionally, the study highlights how different distributional assumptions impact risk estimates, demonstrating the importance of selecting appropriate models for financial data analysis. Furthermore, we illustrate how these improved risk assessment techniques can assist investors and portfolio managers in making more informed decisions regarding risk exposure. By integrating these methods into risk management frameworks, financial professionals can enhance their ability to anticipate and mitigate adverse market conditions. Ultimately, this research contributes to the ongoing efforts to refine quantitative finance tools, ensuring more reliable and data-driven decision-making in portfolio management.
VL  - 9
IS  - 2
ER  -

Copy | Download