A new log-adjusted polynomial Fréchet model for heavy-tailed PORT-VaR analysis and one-step-ahead-VaR forecasting in finance and economics

Abdussalam Aljadani; Abdussalam Aljadani

doi:10.3934/math.20251187

AIMS Mathematics

2025, Volume 10, Issue 11: 27016-27043. doi: 10.3934/math.20251187

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A new log-adjusted polynomial Fréchet model for heavy-tailed PORT-VaR analysis and one-step-ahead-VaR forecasting in finance and economics

Abdussalam Aljadani ^,

Department of Management, College of Business Administration in Yanbu, Taibah University, Yanbu Governorate, Saudi Arabia

Received: 06 September 2025 Revised: 28 October 2025 Accepted: 13 November 2025 Published: 21 November 2025
MSC : 60E05; 62E10; 62H05; 62P05; 62F10; 62F15

This paper introduced a new statistical model for analyzing extreme risks in economic and financial contexts called the log-adjusted polynomial Fréchet (LAPFr) distribution. The proposed distribution offers enhanced flexibility in capturing heavy-tailed behavior, a hallmark of real insurance and financial datasets. Here, the model was applied to two empirically relevant datasets: Boston housing prices and U.S. reinsurance financial revenues, focusing on tail risk estimation and one-step-ahead value-at-risk (VaR) forecasting. Key actuarial risk measures, including VaR, expected shortfall (ExSh), tail variance (TV), tail mean variance (TMV), mean of order P (MOOP), and peaks over random threshold (PORT-VaR), are computed and analyzed across multiple confidence levels. A risk-adjusted return on capital (RAROC) assessment further illustrates the trade-off between return and tail risk, offering practical insights for risk managers and insurers. The number of exceedances above VaR thresholds was examined both numerically and graphically, revealing patterns in the frequency and severity of extreme events. Finally, the one-step-ahead VaR forecast in finance and economics were presented as a part of the risk analysis process.
- actuarial risk,
- economic data,
- finance data,
- peaks over a random threshold Value-at-Risk,
- risk analysis,
- risk-adjusted return on capital,
- Value-at-Risk
Citation: Abdussalam Aljadani. A new log-adjusted polynomial Fréchet model for heavy-tailed PORT-VaR analysis and one-step-ahead-VaR forecasting in finance and economics[J]. AIMS Mathematics, 2025, 10(11): 27016-27043. doi: 10.3934/math.20251187

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Abstract

This paper introduced a new statistical model for analyzing extreme risks in economic and financial contexts called the log-adjusted polynomial Fréchet (LAPFr) distribution. The proposed distribution offers enhanced flexibility in capturing heavy-tailed behavior, a hallmark of real insurance and financial datasets. Here, the model was applied to two empirically relevant datasets: Boston housing prices and U.S. reinsurance financial revenues, focusing on tail risk estimation and one-step-ahead value-at-risk (VaR) forecasting. Key actuarial risk measures, including VaR, expected shortfall (ExSh), tail variance (TV), tail mean variance (TMV), mean of order P (MOOP), and peaks over random threshold (PORT-VaR), are computed and analyzed across multiple confidence levels. A risk-adjusted return on capital (RAROC) assessment further illustrates the trade-off between return and tail risk, offering practical insights for risk managers and insurers. The number of exceedances above VaR thresholds was examined both numerically and graphically, revealing patterns in the frequency and severity of extreme events. Finally, the one-step-ahead VaR forecast in finance and economics were presented as a part of the risk analysis process.

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