摘要：

The paper is twofold. The first aim is to study combined stochastic control and optimal stopping problem. A simple but useful verification theorem for combined control problem is stated. The next result gives a characterization of the value function of the problem as a unique viscosity solution to the associated Hamilton-Jacobi-Bellman variational inequality. The problem is illustrated on a financial application of optimal consumption and optimal stopping. In the second part, the results of the first part are used in order to solve a combined stochastic control and impulse control problem. In turn, this problem can be reduced to an iterative sequence of combined stochastic control and optimal stopping problems. The quasi-variational inequality associated with the problem of portfolio optimization with both fixed and proportional transaction costs is solved numerically with the help of proposed method.

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