Optimal portfolio choice under green transition timing risk

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.