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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 91, 2019 - Issue 7: Hammamet Stochastic Analysis 2017
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Articles

Mean-field stochastic control with elephant memory in finite and infinite time horizon

Nacira AgramDepartment of Mathematics, University of Oslo, Oslo, Norway;Department of Mathematics, Linnaeus University (LNU), Växjö, SwedenView further author information
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Bernt ØksendalDepartment of Mathematics, University of Oslo, Oslo, NorwayCorrespondence[email protected]
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Pages 1041-1066 | Received 25 Apr 2018, Accepted 20 Jun 2019, Published online: 02 Jul 2019

References

  • N. Agram, S. Haadem, B. Øksendal, and F. Proske, A maximum principle for infinite horizon delay equations, SIAM J. Math. Anal. 45(4) (2013), pp. 2499–2522.
  • N. Agram and B. Øksendal, Infinite horizon optimal control of forward–backward stochastic differential equations with delay, J. Comput. Appl. Math. 259 (2014), pp. 336–349.
  • N. Agram and B. Øksendal, Malliavin calculus and optimal control of stochastic Volterra equations, J. Optim. Theory Appl. 167(3) (2015), pp. 1070–1094. doi:10.1007/s10957-015-0753-5. arXiv:1406.0325.
  • N. Agram and B Øksendal, Model uncertainty stochastic mean-field control (2018), arXiv:1611.01385v9, to appear in Stochastic Anal. Appl.
  • N. Agram and B Øksendal, Stochastic control of memory mean-field processes, Appl. Math. Optim. 79(1) (2019), pp. 205–206. doi:10.1007/s00245-017-9425-1. http://arxiv.org/abs/1701.01801v5 “Correction to: Stochastic control of memory mean-field processes” Applied Mathematics and Optimization 2018, doi:10.1007/s00245-018-9483-z.
  • N. Agram, A. Bachouch, B. Øksendal, and F Proske, Singular control and optimal stopping of memory mean-field processes (2018), arXiv:1802.05527.
  • N. Agram and E.E. Røse, Optimal control of forward–backward mean-field stochastic delay systems, Afr. Mat. 29(1–2) (2018), pp. 149–174.
  • N. Agram, B. Øksendal, and S Yakhlef, New approach to optimal control of stochastic Volterra integral equations (2017), arXiv: 1709.05463v2, to appear in Stochastics.
  • R. Carmona and F. Delarue, Mean-field forward–backward stochastic differential equations, Electron. Commun. Prob. 18(68) (2013), pp. 1–15.
  • R. Carmona and F. Delarue, Probabilistic Theory of Mean Field Games with Applications (I), Springer, Berlin, 2018.
  • L. Chen and Z. Wu, Maximum principle for the stochastic optimal control problem with delay and application, Automatica 46 (2010), pp. 1074–1080.
  • K. Dahl, S. Mohammed, B. Øksendal, and E. Røse, Optimal control of systems with noisy memory and BSDEs with Malliavin derivatives, J. Funct. Anal. 271(2) (2016), pp. 289–329. doi:10.1016/j.jfa.2016.04.031
  • E.B. Dynkin, Path processes and historical superprocesses, Probab. Theory Rel. Fields 90(1) (1991), pp. 1–36.
  • M. Fuhrman and H. Pham, Randomized and backward SDE representation for optimal control of non-Markovian SDEs, Ann. Appl. Prob. 25(4) (2015), pp. 2134–2167.
  • H Kunita, Stochastic differential equations based on Lévy processes and stochastic flows of diffeomorphisms, in Real and Stochastic Analysis. Trends in Mathematics, M.M. Rao, ed., Birkhauser, Boston, MA, 2004, pp. 305–373.
  • Q. Meng and Y. Shen, Optimal control of mean-field jump-diffusion systems with delay: A stochastic maximum principle approach, J. Comput. Appl. Math. 279 (2015), pp. 13–30.
  • S.E.A. Mohammed, Stochastic Functional Differential Equations, Research Notes in Mathematics; 99. Pitman (Advanced Publishing Program), Boston, MA, 1984.
  • B. Øksendal, A. Sulem, and T. Zhang, Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations, Adv. Appl. Probab. 43 (2011), pp. 572–596.

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