Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients

Boualem Djehiche, Said Hamadène (), Ibtissem Hdhiri () and Helmi Zaatra ()
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Said Hamadène: LMM, Le Mans University, 72085 Le Mans, Cedex 9, France
Ibtissem Hdhiri: Faculty of Sciences of Gabès, LR17ES11, Tunisia
Helmi Zaatra: Faculty of Sciences of Gabès, LR17ES11, Tunisia

Mathematics of Operations Research, 2022, vol. 47, issue 1, 665-689

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.

Keywords: Primary: 60G40; 60H10; 62L15; 93E20; optimal impulse control; execution delay; infinite horizon; Snell envelope; stochastic control; optimal stopping time; backward stochastic differential equations (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:1:p:665-689

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