Optimization of dynamic trading strategies in carbon markets: A decision framework based on Stackelberg game and prospect theory

The carbon quota trading system, as a globally recognized carbon emission reduction mechanism, has been implemented in many countries. Predicting the optimal trading price, volume, and timing for carbon emission rights traders within the compliance period, which can guide them to maximize their economic benefits, remains unresolved. We innovatively construct a leader-follower optimization model that considers participants’ bounded rationality, multi-participant behavioral interactions, and price stochasticity. We use prospect theory to characterize participants’ risk sensitivity and a Stackelberg game model to determine optimal trading strategies maximizing prospect utility. Given carbon prices’ influence on trading decisions, we apply stochastic differential equations to forecast prices and identify optimal timing. Numerical experiments covering the carbon markets of Beijing, Chongqing, Hubei and the European Union verify the effectiveness of the rolling-window geometric Brownian motion (GBM) model in predicting carbon prices across diverse market environments. Case studies of two enterprises with actual trading records further confirm that the proposed optimal strategy can significantly improve the prospect utility of both buyers and sellers. Sensitivity analysis indicates that stronger loss aversion among participants in profitable scenarios reduces total utility for both sides. Conversely, a greater tendency to overestimate low-probability gains (or losses) or underestimate high-probability gains (or losses) leads to lower optimal trading price, higher trading volume, earlier trading timing, and a decline in total utility. In addition, increasing buyers’ net profit per unit of product or raising government subsidies to sellers can effectively boost trading volume and total utility, thereby enhancing market activity. This study also finds that when both buyers and sellers hold high psychological expectations of marginal returns, they are more likely to exhibit higher trading prices, lower trading volumes and later trading times.