An application of reflected diffusions to the problem of choosing between hydro and thermal power generation

It is shown that a certain type of stochastic control problems has a solution (optimal stochastic process) which can be realized as a diffusion with vertical reflection on the boundary of a planar set. The stochastic control problem is motivated by the specific question whether further expansion of the electricity supply system should be based on thermal power (where only fuel costs are taken into account) or on hydro power (where only the initial construction costs are considered), given a stochastic demand.

Solving Singular Control from Optimal Switching

Singular stochastic control, Optimal switching, Dynkin’s game, Reversible investment, Smooth fit principle,