@article{Alharbi2026, 
author = {Sana Abdulkream Alharbi and Mohamed Abd Allah El-Hadidy},
title = {A multivariate discrete Wiener range distribution with truncation: Theory, reliability properties, and applications to constrained financial markets},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {3563-3593},
keywords = {discrete range modeling, bounded price dynamics, truncated stochastic distributions, reliability measures, range-based volatility},
url = {https://www.sciopen.com/article/10.3934/math.2026146},
doi = {10.3934/math.2026146},
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.}
}