Uncertainty Quantification and Human-Centric Risk Control via Neural–PDE Integration in Complex Volatile Systems

Subject Areas : Financial Mathematics

hosein esmaili ¹ , Mohammad Ali Afshar Kazemi ^{2 *} , reza radfar ³ , nazanin pilevari ⁴

1 - Department of Industrial Management, Science and Research Branch, Islamic Azad University. Tehran, Iran.
2 - Department of Industrial Management, Science and Research Branch, Islamic Azad University. Tehran, Iran.
3 - Department of Industrial Management, Science and Research Branch, Islamic Azad University. Tehran, Iran.
4 - Department of Industrial Management, Science and Research Branch, Islamic Azad University. Tehran, Iran.

Accepted : 2025-06-13 Published : 2025-04-23

Keywords:

Abstract :

This article introduces an integrated approach for addressing uncertainty and improving human-oriented risk control by combining differential equation modeling with neural and fuzzy logic enhancements. Differential equation modeling provides a structured mathematical foundation for capturing price dynamics over time, while neural and fuzzy logic components adaptively adjust the model to account for nonlinear behaviors and uncertain market signals. The proposed framework is applied within volatility-aware trading strategies, comparing fixed-exposure and downside-scaled momentum approaches. Using daily data from five major digital currencies spanning 2016 to 2024, the model demonstrates improved prediction accuracy and controlled exposure under volatile conditions. While the adaptive strategy offers reduced drawdowns and more stable weight distributions, it does not universally outperform in return-to-risk metrics. However, the integrated system consistently shows better alignment with market risk regimes, particularly in directional accuracy, confidence calibration, and drawdown control enhancing its practical viability for real-world deployment.