Optimal Extraction Under Endogenous Degradation Risk

We study the optimal extraction of a non-renewable resource under an endogenous risk of irreversible degradation. The extractor faces a stochastic switching time at which extraction costs permanently increase, with the hazard rate of this transition depending on the current extraction intensity. As a result, faster extraction not only accelerates depletion but also raises the probability of entering a high-cost regime. We formulate the problem as an optimal control model with a control-dependent hazard process and derive a deterministic equivalent representation. Although extraction before and after degradation is individually trivial, their coupling through the endogenous hazard generates a nonlinear control problem. We provide an explicit characterization of the optimal extraction policy and show that degradation risk fundamentally alters the optimal depletion path. In contrast to the deterministic benchmark, optimal extraction becomes smoother over time, as the decision maker trades off immediate profits against the expected increase in future costs. The analysis highlights how endogenous operational risk can discipline extraction incentives and offers new insights into the sustainable management of exhaustible resources under technological fragility.