This review chapter explores how modern data-driven methods can deepen our understanding of unstable financial environments. The chapter focuses on the combined use of wavelet transforms and stochastic modeling to analyze complex, irregular, and rapidly changing financial signals across multiple time scales. It examines how Machine Learning techniques enhance these models by improving pattern recognition, volatility estimation, and predictive accuracy in uncertain market conditions. Through an assessment of recent methodological advances and relevant applications, the chapter highlights how integrating ML with wavelet-based stochastic frameworks can support more informed decision-making, provide early indications of systemic stress, and strengthen analytical tools used in financial research. The study provides a consolidated perspective to support more adaptive and data-driven financial analysis.