Optimal installation of solar panels with price impact: A solvable singular stochastic control problem

We consider a price-maker company which generates electricity and sells it in the spot market. The company can increase its level of installed power by irreversible installations of solar panels. The electricity price evolves as an Ornstein Uhlenbeck process, whose drift is negatively impacted by the current level of the company s installed power. The company aims at maximizing the total expected profits from selling electricity in the market, net of the total expected proportional costs of installation. This problem is modeled as a two-dimensional degenerate singular stochastic control problem. We find that the optimal installation strategy is triggered by a curve which separates the waiting region, where it is not optimal to install additional panels, and the installation region, where it is. Such a curve is the unique strictly increasing solution of a first-order ordinary differential equation. Finally, we show numerically the dependence of the optimal installation strategy on the model s parameters.