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Research Article
Quantifying uncertainty in stochastic process with jumps using deep learning (DL)W. Nangolo1*, R.B. Gnitchogna2
1Department of Computing, Mathematical & Statistical Science, University of Namibia, Madume Ndemufao Ave, Windhoek, Namibia * Corresponding Author. Email: [email protected] ARTICLE INFO Journal: International Journal of Advances in Applied Mathematics and Mechanics (IJAAMM) Volume: 13 | Issue: 4 | Pages: 1–15 Issue date: June 2026 License: Open Access (CC BY-NC-ND 3.0) DOI: 10.26541/ijaamm.2026.130401 ARTICLE HISTORY Received: 25 September 2025 Revised: 20 February 2026 Accepted: 3 March 2026 Published online: March 2026 AbstractUncertainty quantification is crucial for reliable deep learning applications, particularly in financial time series where data noise and model limitations introduce significant uncertainty. This study enhances deep learning-based uncertainty quantification by integrating jump diffusion processes into models, building on recent advancements. Asset price dynamics are modeled using a stochastic differential equation incorporating a jump component. This SDE generates data for training recurrent neural networks (LSTMs/GRUs). Four deep learning-based uncertainty quantification techniques are then applied: Probabilistic Neural Networks, Bayesian Neural Networks, Monte Carlo Dropout, and Deep Ensembles. The framework is applied to European call option pricing. The research evaluates these models’ effectiveness in predicting option prices and providing robust predictive uncertainty measures, demonstrating their utility for financial modeling and risk management in jump-prone assets. KeywordsUncertainty Quantification • Deep Learning (DL) • Stochastic Differential equation • Jump Process • Probabilistic Neural Networks (PNN) • Bayesian Neural Networks (BNN) • Monte Carlo Dropout (MC Dropout) • Deep Ensembles (DE) MSC (2020)60G35 • 68T20 • 60H05 • 60G40 • 68T05 • 62F15 How to CiteNangolo, W., and Gnitchogna, R.B. (2026). Quantifying uncertainty in stochastic process with jumps using deep learning (DL). International Journal of Advances in Applied Mathematics and Mechanics, 13(4), 1–15. https://doi.org/10.26541/ijaamm.2026.130401 © 2026 The Author(s). This article is distributed under the Creative Commons Attribution NonCommercial NoDerivatives License. |
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