Singular stochastic control, linear diffusions, and optimal stopping: A class of solvable problems (Q2706171)

This paper regards a class of singular control problems. It stakes a set of condition under which the optimal policy and its value can be derived in terms of the minimal \(r\)-excessive functions of the controlled diffusion, and demonstrates that the optimal policy is of the standard local time type. Further, a set of smoothness condition are presented under which the value function is increasing and concave. Under these conditions, increased stochastic fluctuations decrease the value and increase the optimal threshold, thus postponing the exercise of the irreversible policy. A connection between singular control and optimal stopping is given. The marginal value of the singular control problem coincides with the value of the associated stopping problem if 0 is not a regular boundary for the controlled diffusion.