Finite horizon stochastic optimal switching and impulse controls with a viscosity solution approach

Abstract

A stochastic optimal switching and impulse control problem in a finite horizon is studied. The continuity of the value function, which is by no means trivial, is proved. The Bellman dynamic programming principle is shown to be valid for such a problem. Moroever, the value function is characterized as the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation.

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