Impulse Control of Multidimensional Jump Diffusions

TL;DR

This paper investigates the regularity of the value function in an infinite-horizon impulse control problem involving multidimensional jump diffusions, showing regularity results similar to diffusion cases despite infinite-activity jumps.

Contribution

It establishes regularity properties of the value function for multidimensional jump diffusions with infinite activity, extending known results from diffusion processes.

Findings

Value function has regularity comparable to diffusion cases.

Regularity holds under certain integrability conditions for jumps.

Results apply to infinite-horizon discounted cost problems.

Abstract

This paper studies regularity property of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly `infinite-activity' jumps. Surprisingly, despite these jumps, we obtain the same degree of regularity as for the diffusion case, at least when the jump satisfies certain integrability conditions.