Stochastic Delay Differential Equations With Wavelet and Curvelet Approaches for Crisis Prediction and Financial Instability

Le résumé fourni par la source

Financial crises emerge from delayed behavioral responses, multi-scale market movements, and the directional spread of shocks across global economic systems. Traditional linear or equilibrium-based models overlook these dynamics because they assume instant adjustment and stable patterns. This chapter presents a unified approach that integrates Stochastic Delay Differential Equations (SDDEs) with wavelet multiresolution analysis and curvelet-based directional methods to enhance the capture of crisis dynamics. SDDEs represent policy lags and feedback delays, wavelets reveal short-term volatility versus long-term cycles, and curvelets trace how shocks propagate across sectors and countries. Through theory, model comparisons, and case studies including the 2008 crash, the COVID-19 shock, the 2015 Chinese turmoil, and the 2022 geopolitical disruption, the chapter shows how SDDE → Wavelet-SDDE → Curvelet-SDDE provides increasing clarity and predictive value for early warning systems and systemic risk assessment.

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