Carbon-penalised portfolio insurance strategies in a stochastic factor model with partial information

We investigate optimal proportional portfolio insurance (PPI) strategies aimed at reducing exposure to carbon intensive stocks. PPI strategies enable investors to mitigate downside risk while retaining the potential for upside gains. In this paper we determine the PPI strategies to maximise the expected utility of the terminal cushion, where the terminal cushion is penalised proportionally to the realised volatility of stocks issued by firms operating in carbon-intensive sectors. We model the risky assets' dynamics using geometric Brownian motions whose drift rates are modulated by an unobservable common stochastic factor to capture market-specific or economy-wide state variables that are typically not directly observable. Using the classical stochastic filtering theory, we formulate a suitable optimisation problem and solve it for the CRRA utility function. We characterise optimal carbon-penalised PPI strategies and optimal value functions under full and partial information. We also carry a numerical analysis showing that the proposed strategy reduces carbon-emissions intensity without compromising financial performance.