Stochastic Modeling and Dynamic Optimization for the Long-Term Sustainability of Energy Savings in Demand-Response Systems
Received: 4 November 2025 | Revised: 27 November 2025 | Accepted: 13 December 2025 | Online: 21 January 2026
Corresponding author: Rayner Ricaurte Parraga
Abstract
The global energy transition critically depends on the effectiveness and long-term persistence of energy-saving measures. However, traditional evaluation models tend to be deterministic, failing to capture the stochastic nature of phenomena such as consumer fatigue and the “rebound effect.” This study proposes a rigorous mathematical framework based on stochastic optimal control. We introduce the Dynamic Sustainability Coefficient (DSC), ψ(t), which is modeled using an Ornstein-Uhlenbeck-type Stochastic Differential Equation (SDE). The net savings maximization problem is solved using the Hamilton-Jacobi-Bellman (HJB) equation. The numerical results, based on calibrated synthetic data, show that the adaptive optimal control strategy outperforms static strategies, increasing the project's Net Present Value (NPV) by 20.1%. A clear methodological workflow is provided to facilitate the model's reproducibility and application in energy policy.
Keywords:
energy analysis, sustainability, stochastic optimal control, Hamilton-Jacobi-Bellman equation, demand response, mathematical modelingDownloads
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Copyright (c) 2026 Julio Villavicencio Mera, Rayner Ricaurte Parraga, Jennyffer Yepez Ramirez, Rossana Ricaurte Parraga, Michelle Zapata Cevallos, Carlos Vaca Coronel, Jesus Verdugo Arcos
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