Carbon-Penalised Portfolio Insurance Strategies in a Stochastic Factor Model with Partial Information

ArXiv ID: 2511.19186 “View on arXiv”

Authors: Katia Colaneri, Federico D’Amario, Daniele Mancinelli

Abstract

Given the increasing importance of environmental, social and governance (ESG) factors, particularly carbon emissions, we investigate optimal proportional portfolio insurance (PPI) strategies accounting for carbon footprint reduction. PPI strategies enable investors to mitigate downside risk while retaining the potential for upside gains. This paper aims to determine the multiplier 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 classical stochastic filtering theory, we formulate a suitable optimization problem and solve it for 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 incomplete information. Finally, we carry a numerical analysis showing that the proposed strategy reduces carbon emission intensity without compromising financial performance.

Keywords: Proportional Portfolio Insurance (PPI), ESG, Carbon Emissions, Stochastic Filtering, Geometric Brownian Motion, Portfolio

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper employs dense mathematical theory including stochastic filtering (Kalman filter), dynamic programming, and partial information optimization under CRRA utility, indicating high math complexity. However, the empirical analysis is based on numerical simulations rather than real-world backtesting or heavy data implementation, resulting in lower empirical rigor.

  flowchart TD
    A["Research Goal<br>Find Optimal Carbon-Penalised<br>Portfolio Insurance Strategy"] --> B["Model Setup<br>Risky Assets + Unobservable<br>Stochastic Factor"]
    B --> C["Methodology<br>Stochastic Filtering +<br>CRRA Utility Optimization"]
    C --> D{"Information State"}
    D --> E["Full Information<br>Optimal Solution"]
    D --> F["Partial Information<br>Filtered Estimates"]
    E --> G["Computation & Analysis<br>Numerical Simulation<br>Utility Comparison"]
    F --> G
    G --> H["Key Outcomes<br>✓ Reduced Carbon Intensity<br>✓ No Financial Performance Loss<br>✓ Quantified Information Loss"]