# 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.

## Key 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.