A novel nonlinear grey Bernoulli model based on recursive regression and pension insurance fund forecast analysis

China’s accelerating population aging places heavy fiscal pressure on the pension insurance system, challenging its long-term sustainability. Reliable forecasting is therefore essential for informed policy design and fiscal risk management. This paper develops a recursive nonlinear grey Bernoulli model (RNGBM) that integrates the Bernoulli nonlinear differential structure with a recursive updating mechanism and embeds a memory factor to enhance adaptability to new information and sudden policy shifts. Using China’s pension fund data (2010–2024), the RNGBM is evaluated against other grey models (GM(1,1), RGM, NGBM) and exponential smoothing based on mean absolute percentage error (MAPE), and further applied to short-term forecasting and fiscal risk assessment under aging scenarios. The RNGBM consistently outperforms other models. Forecasts suggest that while the fund size will grow over the next three years, expenditure growth will exceed revenue growth, reflecting structural risks driven by demographic aging and policy adjustments. This imbalance could accelerate balance depletion, threatening long-term solvency without timely interventions. The RNGBM provides policymakers with a more responsive and robust tool for forecasting pension fund dynamics, supporting evidence-based fiscal governance, optimized resource allocation and proactive reforms to maintain system solvency. This paper is the first to combine the Bernoulli differential structure with a recursive updating and memory-enhanced mechanism, forming a nonlinear recursive grey framework. The RNGBM not only improves methodological accuracy but also demonstrates practical utility in addressing fiscal sustainability challenges in aging societies.