<p>In the era of the Paris Agreement and global ambitions to reduce carbon emissions, an increasing amount of investments must align with net-zero targets to finance the transition towards a low-carbon future. This article presents two novel approaches for investors to align their portfolios with net-zero targets. In this context, we solve two stochastic optimal control problems. Both problems aim to maximize the expected portfolio log-return while (I) simultaneously minimizing the time-weighted portfolio carbon footprint, or (II) minimizing the time-weighted quadratic (relative) deviation from a net-zero target path. For both problems, we find optimal investment strategies. In the first problem, the optimal strategy is obtained from the optimal investment strategy without considering (I) and (II) by a simple drift adjustment, while the second problem requires a drift and covariance adjustment. Our work generalizes selected results from other authors. When applied to real-world data, our strategies significantly reduce portfolio emissions while maintaining comparable financial performance to the unadjusted solution. In total, our strategies enable investors to align their portfolios with self-determined net-zero targets, and they provide a theoretical justification for drift and covariance adjustments for practitioners.</p>