  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.
