An optimal control model for reducing and trading of carbon emissions

A stochastic optimal control model of reducing and trading for carbon emissions is established in this paper. With considerations of reducing the carbon emission growth and the price of the allowances in the market, an optimal policy is searched to have the minimum total costs to achieve the agreement of emission reduction targets. The model turns to a two-dimension HJB equation problem. By the methods of reducing dimension and Cole–Hopf transformation, a semi-closed form solution of the corresponding HJB problem under some assumptions is obtained. For more general cases, the numerical calculations, analysis and comparisons are presented.