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Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients

Author

Listed:
  • Boualem Djehiche

    (Department of Mathematics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden)

  • 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)

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.

Suggested Citation

  • Boualem Djehiche & Said Hamadène & Ibtissem Hdhiri & Helmi Zaatra, 2022. "Infinite Horizon Stochastic Impulse Control with Delay and Random Coefficients," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 665-689, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:665-689
    DOI: 10.1287/moor.2021.1145
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    References listed on IDEAS

    as
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