Monte Carlo Methods for Uncertainty and Risk Assessment: A Methodological Review Across Engineering and Applied Statistics

Abstract

This paper presents a methodological review of Monte Carlo methods as a consolidated toolkit for uncertainty and risk assessment in engineering and applied statistics. Monte Carlo simulation has become one of the most widely adopted stochastic approaches for analyzing systems subject to variability, incomplete information, and complex probabilistic dependencies. Based on the examination of 24 representative studies published between 1989 and 2025, this review synthesizes the method’s theoretical foundations, implementation workflows, and major application domains, ranging from structural reliability analysis to financial risk evaluation. Particular attention is devoted to the attributes that underpin its widespread adoption—namely flexibility, interpretability, and robustness in nonlinear and high-dimensional contexts—as well as to intrinsic limitations, including slow convergence rates, dependence on accurate input distributions, and high computational demand. The review further discusses recent methodological advances designed to mitigate these constraints, such as hybrid frameworks integrating Monte Carlo sampling with machine learning techniques and intelligent variance-reduction strategies. Overall, the study provides a comprehensive analytical perspective on the contribution of Monte Carlo methods to decision-support systems and outlines future research directions aimed at enhancing efficiency, scalability, and integration within complex stochastic modeling environments.