A Class of Extended Singular Stochastic Models with Stopping Time

By stochastic analysis method and optimal control theory, the paper discusses a class of singular stochastic control problems with stopping time, introduces a drift parameter into the state and extends the diffusion parameter from 1 to <em<σ</em<. The solution of the variational inequation,together with the optimal strategies are given, i.e. the optimal control and the optimal stopping time. The algorithm also shows that solution is just the optimal cost function.