A mixed singular/switching control problem with gradient constraint and terminal cost for a modulated diffusion

Mark Kelbert, Harold Moreno-Franco

Published 2022-11-23Version 1

In this paper, we study the regularity of the value function associated with a stochastic control problem where two controls act simultaneously on a modulated multidimensional diffusion process. The first is a switching control modelling a random clock. Every time the random clock rings, the generator matrix is replaced by another, resulting in a different dynamic for the finite state Markov chain of the modulated diffusion process. The second is a singular stochastic control that is executed on the process within each regime.