A multivariate discrete Wiener range distribution with truncation: Theory, reliability properties, and applications to constrained financial markets

Sana Abdulkream Alharbi; Mohamed Abd Allah El-Hadidy; Sana Abdulkream Alharbi; Mohamed Abd Allah El-Hadidy

doi:10.3934/math.2026146

AIMS Mathematics

2026, Volume 11, Issue 2: 3563-3593. doi: 10.3934/math.2026146

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Research article

A multivariate discrete Wiener range distribution with truncation: Theory, reliability properties, and applications to constrained financial markets

Sana Abdulkream Alharbi ^1,2,
Mohamed Abd Allah El-Hadidy ^{3
,
,}

1.
Department of Mathematics and Statistics, College of Science in Yanbu, Taibah University, Yanbu Governorate, Saudi Arabia; saaharbi@taibahu.edu.sa
2.
Health and Life Research Center, Taibah University, Madinah, Saudia Arabia
3.
Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, Egypt; melhadidi@science.tanta.edu.eg

Received: 17 November 2025 Revised: 11 January 2026 Accepted: 27 January 2026 Published: 05 February 2026
MSC : 60E05, 60J70

We developed a multivariate discrete range distribution derived from the Wiener process to model high-low price dynamics of multiple assets observed at discrete times and subject to market imposed bounds. The model provides closed-form expressions for the joint PMF, CDF, survival and hazard functions, reversed and second order failure rates, moments, stress-strength reliability, and a full system of multivariate order statistics. A truncated version of the distribution was also established to account for realistic price limit regimes, showing how probability mass redistributes within constrained domains. These theoretical properties were supplemented by a numerical study based on real high-low data and confirmed that the model can capture clustered volatility, attenuation of tail risk, and joint range behavior more precisely than unconstrained formulations. The proposed framework offers a mathematically coherent and computationally practical tool for the analysis of range-based behavior in constrained financial markets.
- discrete range modeling,
- bounded price dynamics,
- truncated stochastic distributions,
- reliability measures,
- range-based volatility
Citation: Sana Abdulkream Alharbi, Mohamed Abd Allah El-Hadidy. A multivariate discrete Wiener range distribution with truncation: Theory, reliability properties, and applications to constrained financial markets[J]. AIMS Mathematics, 2026, 11(2): 3563-3593. doi: 10.3934/math.2026146

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Abstract

We developed a multivariate discrete range distribution derived from the Wiener process to model high-low price dynamics of multiple assets observed at discrete times and subject to market imposed bounds. The model provides closed-form expressions for the joint PMF, CDF, survival and hazard functions, reversed and second order failure rates, moments, stress-strength reliability, and a full system of multivariate order statistics. A truncated version of the distribution was also established to account for realistic price limit regimes, showing how probability mass redistributes within constrained domains. These theoretical properties were supplemented by a numerical study based on real high-low data and confirmed that the model can capture clustered volatility, attenuation of tail risk, and joint range behavior more precisely than unconstrained formulations. The proposed framework offers a mathematically coherent and computationally practical tool for the analysis of range-based behavior in constrained financial markets.

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