SIAM Journal on Control and Optimization, Vol.48, No.6, 3781-3804, 2010
A SINGULAR CONTROL PROBLEM WITH DISCRETIONARY STOPPING FOR GEOMETRIC BROWNIAN MOTIONS
In this paper, we discuss a combined singular control problem with discretionary stopping for geometric Brownian motions. By the method of penalization, we solve the degenerate variational inequality associated with this problem. Its solution v coincides with the value function and, by the concavity of v, an optimal control is shown to exist.
Keywords:geometric Brownian motion;variational inequality;viscosity solutions;singular stochastic control;optimal stopping