Optimal design of carbon-penalized proportional portfolio insurance strategies in a partially observable market model

Given the increasing importance of environmental, social and governance (ESG) factors, particularly carbon emissions, we investigate an optimal investment problem associated with proportional portfolio insurance (PPI) strategies that account for carbon risk.
PPI strategies enable investors to mitigate downside risk while retaining the potential for upside gains. The latter goals are achieved by maintaining the exposure to the risky assets proportional to the so-called cushion, namely the difference between the portfolio value and the present value of the guaranteed amount.
This paper aims to determine the exogenous parameters of the PPI strategy 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 reduce this optimal problem with partial information to the one with complete information and solve it for the CRRA utility function. We characterise optimal carbon-penalised PPI strategies and optimal value functions under full and partial information and quantify the loss of utility due to incomplete information. Finally, we calibrate the proposed model using on real data and show that our new strategy reduces emission intensities without compromising financial performance.