Pollution Control Under Uncertainty: Integrating Optimal Control Theory and Value of Information

This study analyses the economic value of information in dynamic environmental decision-making, focusing on how pre-decision resolution of parameter risk affects optimal policy paths. We develop a framework that integrates optimal control (OC) theory with the Value of Information (VoI) concept. Using a continuous-time pollution control model, we analytically derive VoI for different types of uncertainty - initial conditions and model parameters - highlighting how the structure of uncertainty affects its value. We introduce a benchmark "naive certainty-equivalent" policy that ignores uncertainty and quantify the resulting excess in the expected value of perfect information. Our results show that VoI depends on whether uncertainty changes the marginal intertemporal trade-off faced by the decision maker. Information about the initial pollution stock has no value in the present linear-quadratic setting, because it affects welfare levels but not the optimal policy path. By contrast, information about the environmental absorption rate has strictly positive value for any non-degenerate distribution, because it changes the effective persistence of pollution and therefore the optimal balance between current production and future environmental damages. The proposed approach provides a tractable and extensible method for quantifying VoI in intertemporal environmental management problems under parametric risk.