Optimal policies for some n-dimensional singular stochastic control problems

摘要: We consider a singular stochastic control problem with radially symmetric running cost. show that the value function is smooth, non-action region ball and has an explicit solution in terms of power series. Also, for ergodic class admissible processes constrained to Brownian motions reflected normally at boundary some open, connected Caccioppoli set, we existence, regularity basic properties optimal domains using geometric measure-theoretic approach.