On a mixed singular/switching control problem with multiples regimes

Mark Kelbert, Harold A. Moreno-Franco

Published 2020-06-24Version 1

This paper studies the mixed singular/switching stochastic control problem for a multidimensional diffusion with multiples regimes in a bounded domain. Using probabilistic, partial differential equation (PDE) and penalized techniques, we show that the value function associated with this problem agrees with the solution to a Hamilton-Jacobi-Bellman (HJB) equation. In that way, we see that the regularity of the value function is $\hol^{0,1}\cap\sob^{2,\infty}_{\loc}$.