Existence of singular optimal control laws for stochastic differential equations

Abstract

This paper studies the existence of a control problem where the state is governed by a stochastic differential equation allowing both classical control and singular control. By transforming it into a new problem that involves only classical control, it is shown that there exists an optimal control where the classical control variable is in Markovian form and the increment of the singular control variable on any time interval is adapted to the state process on the same time interval.