A leavable bounded-velocity stochastic control problem.
The paper studies solutions to optimal control of the drift of a diffusion process that can be stopped arbitrarily. Accordingly, the minimized objective function of the control problem consists of the expected running cost and exit cost terms. Both fully observed and partially observed state process cases are considered. In the fully observed case, the bang-bang controls and the optimal stopping regions are identified for a class of strictly convex cost functions. The value function is derived and the optimal behavior is shown to be heavily dependent upon the relative weight of exit cost. The control of a partially observed state process is considered for cost functions of polynomial growth, separately for finite and infinite horizon cases. It is established that when stopping at a given level of the state is optimal in the infinite horizon problem, doing so is also optimal in any finite horizon problem as well. Further, it is shown that for any horizon, finite or infinite, the optimal stopping region of the fully observed control is included in the one of the partially observed control.
scientific article; zbMATH DE number 2138961
scientific article