Robust consumption and portfolio optimization under climate risk and uncertainty

This paper examines a robust consumption-investment problem for a representative investor endowed with Epstein-Zin stochastic differential utility over an infinite horizon. The financial market comprises green and brown risky assets, each exposed to climate-related and macroeconomic shocks, while brown assets are additionally subject to policy risk induced by climate regulation. The investor is ambiguity-averse and particularly concerned about model uncertainty regarding these risks. Using a robust control method based on relative entropy, we derive a semi-closed-form solution for the case of unit elasticity of intertemporal substitution (EIS) and an approximate solution for the case where EIS is less than one. Our results indicate that optimal portfolio strategies are primarily influenced by ambiguity regarding price diffusion in both green and brown assets. Furthermore, we demonstrate that the interplay between ambiguity aversion and diversification motives leads the investor to overweight green assets, resulting in a gradual transition from high-carbon to low-carbon production. For investors with EIS less than one, the negative income effect dominates the positive intertemporal substitution effect due to the downward jump in extreme Poisson events, leading to a reduction in the current consumption-to-wealth ratio. Finally, we quantify the wealth losses resulting from ignoring ambiguity and show that most of these losses stem from ignoring the ambiguity about the diffusion risk of brown assets. By integrating climate-related risks and ambiguity aversion into a robust consumption and portfolio framework, this study provides novel insights for investors navigating the transition to a low-carbon economy.