Innovation, commutation et contr\^ole impulsionnel en horizon infini

TL;DR

This paper addresses an infinite horizon impulse control problem by extending double barrier reflected backward stochastic differential equations, using properties of the Snell envelope to establish the existence of continuous process pairs.

Contribution

It extends finite horizon results to the infinite horizon case for impulse control using advanced stochastic differential equations and the Snell envelope.

Findings

Established existence of measurable continuous process pairs

Extended double barrier reflected backward stochastic differential equations to infinite horizon

Connected Snell envelope properties to impulse control solutions

Abstract

We consider an impulse control problem in infinite horizon. To solve this problem, we extend to the infinite horizon case results of double barrier reflected backward stochastic differential equations. The properties of the Snell envelope can reduce our problem to show the existence of a pair of measurable continuous processes.