Problems of singular stochastic control with stopping, drift and diffusion
一类具有漂移、扩散及停时的奇异型随机控制

Based on the stochastic calculus and the classical theory of optimal control, this paper generalizes a class of the discounted model of singular stochastic control with stopping time. Drift and diffusion coefficients are introduced into the controlled states to make them the solution of a stochastic differential equation. Meanwhile, the cost function is also generalized. By solving a variational equation, we prove the existence of the optimal control and the optimal stopping time. Moreover, we derive the explicit form for the optimal cost function.