With the advancement of artificial intelligence (AI) and big data technology, traditional financial management faces challenges in meeting modern needs. China's financial sector, although late to start, is embracing AI to mitigate risks like business and credit risks. This study explores risk prediction and avoidance methods in finance using AI. It employs elementary catastrophe theory to analyze dynamic system discontinuity, identifying high-risk periods when the calculated financial stress index (FSI) exceeds 1. Each unit increase in FSI affects its lag period by 0.7327 units. Macro-economic pressure, reflected in the macroeconomic pressure index (MSI), significantly impacts FSI, with the current period having a more pronounced effect than the lag period. Financial institutions must evolve talent into hybrid professionals and invest in AI to enhance risk management while pursuing profitability.