Carbon-aware Optimal Renewable Investment under Uncertainty: A Prospect Theory Analysis

In this paper, we investigate the power generation company's renewable investment problem under renewable uncertainty within the framework of the cap-and-trade policy. This policy regulates the carbon emission levels of such companies by assigning them carbon emission quotas. Previous studies on renewable investment within the cap-and-trade policy framework have predominantly concentrated on solving the expected cost-minimization problem for a risk-neutral consumer using the expected utility theory (EUT). However, empirical evidence suggests that the EUT model may not accurately reflect real-world behaviors. To address this, we propose a prospect theory (PT) model from behavioral economics to gain deeper insight into the power generation company's renewable investment decisions, taking into account their risk preferences. Despite the non-convexity of the PT-based optimization problem of the power generation company, we obtain the optimal solutions by leveraging the unimodal structure of the objective function. Theoretical and numerical results demonstrate that the power generation company's decisions are significantly affected by their risk preferences: 1) the PT power generation company with a higher reference point is more willing to take risks and invest in renewable energy due to the greater expectations compared with the case of a low reference point; 2) the PT power generation company is more willing to invest in renewable energy when the probability of high renewable production is small, due to the probability distortion.