A class of solvable singular stochastic control problems

Abstract

We consider the singular stochastic control problem of a linear, time-homogeneous and regular diffusion process. By relying on a combination of stochastic calculus the classical theory of diffusions, and ordinary nonlinear programming techniques, we find the optimal policies and their value functions in the three most common cases appearing in the applications of singular controls. Especially we demonstrate that the smooth fit principle can be interpreted as an ordinary first order necessary condition for optimality

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