Machine Learning–Augmented Hybrid Risk Management and Deep Uncertainty Quantification in Nepalese Management Systems: Fractional Stochasticity, Wasserstein Robustness, and Rough–Path Neural Filtering
Risk management in Nepal has never been a matter of applying textbook formulas to Himalayan data. The country’s management systems—spanning hydropower consortia in Gandaki, microfinance networks in the Terai, tourism supply chains in Solu-Khumbu, and federal bureaucracies still finding their footing after the 2015 constitutional rupture—operate under uncertainty that standard stochastic calculus refuses to acknowledge. Monsoon persistence stretches across seasons with long-range dependence that Markovian models cannot capture. Remittance corridors from Qatar and Malaysia collapse and reopen with pathwise irregularity that violates the semimartingale assumption underlying Itô calculus. Political transitions—from monarchy to insurgency to federal republic—have produced institutional trajectories of such unbounded variation that classical risk filters simply disintegrate. And through all of this, the data available to Nepalese risk managers is sparse, patchy, and structurally compromised by conflict, earthquake, and repeated administrative reorganization.This paper constructs a comprehensive theoretical framework for machine learning–augmented hybrid risk management and deep uncertainty quantification specifically calibrated to these conditions. We develop four interconnected mathematical pillars. First, neural fractional stochastic risk processes driven by fractional Brownian motion with Hurst exponent H≠1⁄2, where recurrent neural architectures estimate long-memory parameters from incomplete time series and correct the systematic underestimation of tail risk inherent in classical value-at-risk. Second, machine learning–adaptive Wasserstein distributionally robust risk measures, where neural networks learn the shape and radius of ambiguity sets from sparse Nepalese data, yielding tractable worst-case expectations via strong Lagrangian duality. Third, rough–path neural filtering, which combines Lyons’ signature theory with deep learning to track irregular risk cascades across institutional networks whose paths are too rough for standard stochastic integration. Fourth, deep ensemble uncertainty quantification, layering Bayesian neural networks with causal priors into second-order imprecise probability hierarchies that distinguish aleatory, epistemic, and ontological uncertainty.Every structural claim is accompanied by formal definitions, numbered equations, and rigorous proofs. We derive the exact fractional value-at-risk correction for seasonal horizons, prove strong duality for the learned Wasserstein ambiguity set, establish continuity of the neural rough differential equation solution map in the Hölder topology, and decompose predictive variance into its three fundamental constituents. The paper is theoretical and unpublished; no empirical calibration is attempted, though the mathematical specifications are sufficiently tight to guide implementation. All references carry verified DOIs..