A mixed singular/switching control problem with terminal cost for modulated diffusion processes

TL;DR

This paper investigates the regularity of the value function in a complex stochastic control problem involving simultaneous switching and singular controls on modulated diffusion processes, with applications to systems influenced by random regime changes.

Contribution

It introduces a novel analysis of a combined switching and singular control problem with terminal cost for modulated diffusions, expanding understanding of such hybrid control systems.

Findings

Established regularity properties of the value function.

Analyzed the impact of switching controls on diffusion dynamics.

Provided theoretical insights into combined control strategies.

Abstract

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.