  In this paper we consider an energy storage optimization problem in finite
time in a model with partial information that allows for a changing economic
environment. The state process consists of the storage level controlled by the
storage manager and the energy price process, which is a diffusion process the
drift of which is assumed to be unobservable. We apply filtering theory to find
an alternative state process which is adapted to our observation filtration.
For this alternative state process we derive the associated
Hamilton-Jacobi-Bellman equation and solve the optimization problem
numerically. This results in a candidate for the optimal policy for which it is
a-priori not clear whether the controlled state process exists. Hence, we prove
an existence and uniqueness result for a class of time-inhomogeneous stochastic
differential equations with discontinuous drift and singular diffusion
coefficient. Finally, we apply our result to prove admissibility of the
candidate optimal control.
