Reducing the carbon footprint of financial portfolios has become a central challenge in climate finance. A variety of metrics are available to measure portfolio decarbonization, ranging from straightforward year-on-year emission reduction targets to more sophisticated, forward-looking indicators such as Net-Zero frameworks or the Implied Temperature Rise (ITR) score. In this paper, we examine the implications of incorporating such decarbonization constraints into optimal portfolio choice. We propose a methodology to formally integrate portfolio-owned carbon emissions into the dynamic optimization problem and highlight the conceptual distinction between emission reduction targets and cumulative emission constraints. By formalizing these within a unified framework, we highlight their conceptual differences and analyse how each influences optimal investment strategies and long-term sustainability outcomes.
