To meet the targets of the Kyoto Protocol, the European Union established the European Emission Trading Scheme, a mandatory market for carbon emission allowances. This regulatory framework has introduced a market for emission allowances and created a variety of emission-related financial instruments. In this work, we show that the economic mechanism of carbon allowance price formation can be formulated in the framework of competitive stochastic equilibrium models, and we show that its solution reduces to an optimal stochastic control problem. Using this mathematical setup, we identify the main allowance price drivers and show how stochastic control can be used to treat quantitative problems in carbon price risk management.