Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients

Boualem Djehiche; Said Hamadène; Ibtissem Hdhiri; Helmi Zaatra

doi:10.1287/moor.2021.1145

Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients

Boualem Djehiche, Said Hamadène, Ibtissem Hdhiri, Helmi Zaatra

Mathematics

Research output: Contribution to journal › Article › peer-review

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 stochastic process adapted to the Brownian filtration. 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.

Original language	English (US)
Pages (from-to)	665-689
Number of pages	25
Journal	Mathematics of Operations Research
Volume	47
Issue number	1
DOIs	https://doi.org/10.1287/moor.2021.1145
State	Published - Feb 2022

Keywords

Backward stochastic differential equations
Execution delay
Infinite horizon
Optimal impulse control
Optimal stopping time
Snell envelope
Stochastic control

ASJC Scopus subject areas

General Mathematics
Computer Science Applications
Management Science and Operations Research

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10.1287/moor.2021.1145

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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 stochastic process adapted to the Brownian filtration. 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.",

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AU - Zaatra, Helmi

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AB - We study a class of infinite horizon impulse control problems with execution delay when the dynamics of the system is described by a general stochastic process adapted to the Brownian filtration. 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.

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KW - Execution delay

KW - Infinite horizon

KW - Optimal impulse control

KW - Optimal stopping time

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Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients

Abstract

Keywords

ASJC Scopus subject areas

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