ABSTRACT We analyze the problem of a profit‐maximizing electricity producer, subject to carbon taxes, who decides on investments into abatement technologies. We assume that the carbon tax policy is random and that the investment in the abatement technology is divisible, irreversible, and subject to transaction costs. Two frameworks for randomness in taxes are considered. First, we assume a precise probabilistic model for the tax process, namely a pure jump Markov process (so‐called tax‐risk). Second, we analyze the case of a producer who is uncertainty‐averse with respect to the tax evolution and who uses a differential game as conceptual tool to decide on optimal production and investment. We provide a rigorous mathematical treatment of both settings, including the analysis of the associated nonlinear PDEs. Numerical methods are employed to investigate the optimal investment strategies. We find that in the tax‐risk case, investment in abatement technologies is generally lower than in a benchmark scenario with deterministic taxation. Nevertheless, factors such as production technology, investment divisibility, tax rebates, and credibility of the tax policy introduce interesting twists. In contrast, the uncertainty‐averse framework may lead to increased investment as uncertainty rises.