Paper: arXiv 2610.33597

Authors: Emma Kroell, Mogens Steffensen

Abstract

We study an investor’s optimal portfolio choice problem when they account for the impact of a possible future green transition, whose timing is uncertain. We model the green transition as a discontinuity in the stock price processes, driven by a single jump process with constant intensity, in which ‘green’ stocks increase in value and ‘brown’ stocks decrease in value. The investor is ambiguous about the timing of the green transition and designs an investment strategy which is robust to this risk. The investor has constant relative risk aversion preferences over both wealth and model ambiguity, which introduce a multiplicative ambiguity penalty for power utility and an additive ambiguity penalty for log utility. We separate the problem into pre- and post-transition cases, derive the solution, and provide a verification theorem. We further show that the log utility, ambiguity-neutral, and worst-case problems are obtained as special cases of our general problem. In a case study with one green and one brown stock, we show that when the stock prices are positively correlated, an investor who is aware of transition risk increases their investment in the green stock and reduces their investment in the brown stock, compared to when they ignore the possibility of a transition. We illustrate the difference between an ambiguity-averse and a risk-averse investor, and show how an ambiguity-averse investor re-allocates their portfolio as their view on the probability of a green transition changes.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly mathematical framework for optimal portfolio choice under green transition timing risk, incorporating ambiguity aversion. While the theoretical derivations are rigorous and novel, the empirical validation is limited to a single case study without extensive backtesting or real-world data analysis. This places it firmly in the ‘Lab Rats’ quadrant, excelling in theoretical development but needing more empirical grounding.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Portfolio Choice under Green Transition Timing Risk] --> B{Key Methodology: Jump Process Model with Uncertain Timing & Ambiguity Aversion};
    B --> C{Inputs: Green/Brown Stock Prices, Jump Intensity, Investor Preferences (CRRA, Ambiguity Aversion)};
    C --> D[Computational Processes: Separate Pre/Post-Transition Cases, Derive Solution, Verification Theorem];
    D --> E[Key Findings: Increased Investment in Green Stocks, Reduced Brown Stocks under Transition Risk];
    E --> F[Further Findings: Differentiation of Ambiguity-Averse vs. Risk-Averse Investor Allocation; Log Utility & Worst-Case as Special Cases];