We will address stochastic control problems from three different directions. At the first part, we determine the optimal strategy to distribute the dividends, when the underlying capital follows SNLP (spectrally negative L´evy process) and discounting factor is an exponential L´evy process, generally based on Itˆo excursion theory. At the second part, we look at an Hamilton-Jacobi-Bellman equa- tion from a classical stochastic control problem. Considering the implicit derivatives’ constraints and free boundary, we develop a so- called ”Projected semismooth Newton with shooting-like method” and then provide corresponding (superlinear) convergence and error analysis. At the last part, we propose a new stochastic control model on optimally utilizing the renewable energy flexibility in the electricity market. We illustrate a new feasible strategy ”Curve strategy with trigger price” in a classical setting first. Then after establishing boundedness of value function and related verification lemma, we prove the existence and uniqueness of the optimal strategy in a more realistic setting via viscosity solution argument.