Joint Control of Emissions Permit Trading and Production Involving Fixed and Variable Transaction Costs

The use of permit markets to mitigate harmful emissions is on the rise. When participating in such a market, an emitting firm needs to acquire from it permits that cover emissions resulting from production. Thus, it has to simultaneously cope with fluctuating permit prices and random demand, and also juggle between the activities of permit trading and permit-consuming production. We shed light on this complex dynamic control problem, while confronting difficulties brought on by fixed as well as variable transaction costs associated with permit trading. We exploit K-convexity variants that are suitable for two-dimensional control, and achieve the partial characterization of optimal control policies. When the selling of permits is prohibited, we prescribe an (s, S)-type permit purchasing policy. For the more general case involving two-way trading, we find it optimal to carry out trading in a three-interval fashion. Heuristics, including one based on the uncoupling of trading and production activities, are introduced. Their effectiveness has been illustrated in computational studies.