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

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.