To limit the emission of green house gases, a market of emission permits was installed. We aim to model the emission market in order to learn how regulatory decisions have an impact on the market participants. Usually, the behaviour of the participants of the emission market is described by a Nash equilibrium. In a first step, we proved that under certain assumptions their behaviour also satisfies a global optimization problem. The solution of the optimization problem can be characterised by an Hamilton-Jacobi-Bellman equation, which we are going to solve numerically.