Optimal Timing of Carbon-Capture Retrofit on a Mature Offshore Gas Platform under Stochastic EU-ETS Prices and a Stochastic Decommissioning Deadline

We study when the operator of a mature offshore gas platform should retrofit carbon capture and storage when the price of EU Emissions Trading System (EU ETS) allowances is stochastic and a regulatory decommissioning deadline arrives at a random time. The retrofit is irreversible, and once installed it saves the allowances on the avoided emissions until the deadline. We pose the decision as optimal stopping of a geometric Brownian motion killed at an exponential deadline, show that the decommissioning charge cancels from the decision, derive the free-boundary variational inequality, in which the deadline enters with the term $+\lambda\Phi = -\lambda D$, and solve it in closed form for an open-ended retrofit window and numerically for a finite one. The price model is fitted to EU ETS primary-auction clearing prices on 1,343 auction days from January 2018 to 7 May 2024 (EEX auction results as published by the Instrat Foundation; licence and credit in Section 5.1). The monthly volatility is $\hat\sigma = 0.380$; the historical drift, 0.40 per year, exceeds any discount rate and cannot serve as a valuation drift. Investment costs and emissions come from a peer-reviewed study of a North Sea platform; operating costs come from a US DOE/NETL onshore study, used as a stated proxy. With a mean residual life of 12 years the retrofit threshold is 180 €/tCO$_2$, 2.68 times the zero-NPV price and well above the auction price of 69.16 €/tCO$_2$ on 7 May 2024; with a 6-year mean life it rises to 239 €/tCO$_2$. We prove that the threshold rises with the deadline hazard exactly when the annuity on the retrofit capital outweighs the fall in the option premium; at the calibrated costs this holds for every mean residual life below 76 years. The study’s range of capital costs moves the 12-year threshold from 71 to 290 €/tCO$_2$. Each headline number is checked by a grid solution of the variational inequality and by a Monte Carlo simulation of the stopping rule.