Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients

TL;DR

This paper addresses infinite horizon stochastic impulse control problems with delays and random coefficients, employing probabilistic methods like Snell envelopes and backward stochastic differential equations to prove the existence of optimal strategies.

Contribution

It introduces a novel approach to solving impulse control problems with delays and random coefficients using advanced probabilistic tools.

Findings

Existence of optimal strategies established

Applicable to systems with general adapted stochastic dynamics

Utilizes Snell envelope and reflected backward stochastic differential equations

Abstract

We study a class of infinite horizon impulse control problems with execution delay when the dynamics of the system is described by a general adapted stochastic process. The problem is solved by means of probabilistic tools relying on the notion of Snell envelope and infinite horizon reflected backward stochastic differential equations. This allows us to establish the existence of an optimal strategy over all admissible strategies.