<p>This paper explores the theoretical and practical implications of an ESG model for polluting extractive industries. We are investigating an intertemporal decision-making problem in an extractive business, subject to fines for exceeding a regulatory pollution threshold. To minimize negative externalities and maintain compliance with ESG principles, the company must invest in depollution, using a subsidy structure. We present a stochastic nonlinear system-based approach that concurrently defines the optimal profit function, extraction strategy, and ecological investment across a broad spectrum of pollution levels, incorporating the intricate interplay between environmental and economic features. Through a stochastic optimal control problem formulation, CRRA utility function is used to maximize the expected pollution-adjusted net profit controlled by the extraction rate and ecological investment. The findings demonstrate how environmental conditions and laws affect the optimal profitability, extraction, and ecological investment options. Our ESG model allows coordinated dynamics; controls tighten as environmental risk increases, maintaining the system close to the benchmark while maximizing profit. It ensures the trade-offs between environmental protection, control effort, and profit.</p>