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Research Article

Infinite horizon impulse control of stochastic functional differential equations driven by Lévy processes

Received 17 Aug 2020, Accepted 08 Sep 2023, Published online: 04 Oct 2023

References

  • N. Agram and B. Øksendal, Stochastic control of memory mean-field processes, Appl. Math. Optim.79(1) (2019), pp. 181–204.
  • M. Basei, Optimal price management in retail energy markets: an impulse control problem with asymptotic estimates, Math. Meth. Oper. Res. 89(3) (2019), pp. 355–383.
  • A. Bensoussan and J.L. Lions, Impulse Control and Quasivariational Inequalities, Gauthier-Villars, Montrouge, France, 1984.
  • D.P. Bertsekas and S.E. Shreve, Stochastic Optimal Control: The Discrete-time Case, Academic Press, 1978.
  • R. Carmona and M. Ludkovski, Pricing asset scheduling flexibility using optimal switching, Appl. Math. Finance 15(5-6) (2008), pp. 405–447.
  • C. Dellacherie and P.-A. Meyer, Probabilités Et Potentiel, I-IV, Hermann, Paris, 1975.
  • C. Dellacherie and P.-A. Meyer, Probabilités Et Potentiel, V-VIII, Hermann, Paris, 1980.
  • B. Djehiche, S. Hamadène, and I. Hdhiri, Stochastic impulse control of non-markovian processes, Appl. Math. Optim. 61(1) (2010), pp. 1–26.
  • B. Djehiche and S. Hamadène, On a finite horizon starting and stopping problem with risk of abandonment, Int. J. Theoret. Appl. Finance 12(04) (2009), pp. 523–543.
  • B. Djehiche, S. Hamadène, I. Hdhiri, and H. Zaatra, Infinite horizon stochastic impulse control with delay and random coefficients, Math. Oper. Res. 47(1) (2022), pp. 665–689.
  • B. Djehiche, S. Hamadène, and A. Popier, A finite horizon optimal multiple switching problem, SIAM J. Control Optim. 48(4) (2009), pp. 2751–2770.
  • N. El Karoui, Les aspects probabilistes du contrôle stochastique. Ecole d'Eté de SaintFlour IX 1979. Lecture Notes in Math, Berlin, Springer, 1981.
  • N. El-Karoui, C. Kapoudjian, E. Pardoux, S. Peng, and M.C. Quenez, Reflected solutions of backward SDEs and related obstacle problems for PDEs, Ann. Probab. 25(2) (1997), pp. 702–737.
  • S. Hamadène, Reflected BSDE's with discontinuous barrier and application, Stoch. Int. J. Probab. Stoch. Process. 74(3-4) (2002), pp. 571–596.
  • S. Hamadène and J. Zhang, Switching problem and related system of reflected backward SDEs, Stoch. Process. Appl. 120(4) (2010), pp. 403–426.
  • I. Hdhiri and M. Karouf, Optimal stochastic impulse control with random coefficients and execution delay, Stoch. Int. J. Probab. Stoch. Process. 90(2) (2018), pp. 151–164.
  • J. Jönsson and M. Perninge, Finite horizon impulse control of stochastic functional differential equations, SIAM J. Control Optim. 61(2) (2023), pp. 924–948.
  • N. El Karoui and X. Tan, Capacities, measurable selection and dynamic programming part i: Abstract framework. arXiv:1310.3363, 2013.
  • R. Korn, Some applications of impulse control in mathematical finance, Math. Meth. Oper. Res. 50(3) (1999), pp. 493–518.
  • R. Martyr, Finite-horizon optimal multiple switching with signed switching costs, Math. Oper. Res.41(4) (2016), pp. 1432–1447.
  • B. Øksendal and A. Sulem, Applied Stochastic Control of Jump Diffusions, Springer, 2007.
  • B. Øksendal and A. Sulem, Optimal stochastic impulse control with delayed reaction, Appl. Math. Optim. 58(2) (2008), pp. 243–255.
  • J. Palczewski and L. Stettner, Impulsive control of portfolios, Appl. Math. Optim. 56(1) (2007), pp. 67–103.
  • M. Perninge, A finite horizon optimal switching problem with memory and application to controlled sddes, Math. Meth. Oper. Res. 91(3) (2020), pp. 465–500.
  • P. Protter, Stochastic Integration and Differential Equations, 2nd ed. Springer, Berlin, 2004.