References
Agram N, Haadem S, ∅ksendal B, et al. A maximum principle for infinite horizon delay equations. SIAM J Math Anal, 2013, 45: 2499–2522
∅ksendal B, Sulem A. A maximum principle for optimal control of stochastic systems with delay, with applications to finance. In: Optimal Control and Partial Differential Equations—Innovations and Applications. Amsterdam: IOS Press, 2000. 64–79
Shen Y, Meng Q, Shi P. Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance. Automatica, 2014, 50: 1565–1579
Chen L, Wu Z. Maximum principle for the stochastic optimal control problem with delay and application. Automatica, 2010, 46: 1074–1080
Huang J, Shi J. Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations. ESAIM: Control Opt Calc Var, 2012, 18: 1073–1096
Meng Q, Shen Y. Optimal control of mean-field jump-diffusion systems with delay: a stochastic maximum principle approach. J Comput Appl Math, 2015, 279: 13–30
∅ksendal B, Sulem A, Zhang T. Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations. Adv Appl Probab, 2011, 43: 572–596
Peng S, Yang Z. Anticipated backward stochastic differential equations. Ann Probab, 2009, 37: 877–902
Acknowledgements
This work was supported by the Fostering Project of Dominant Discipline and Talent Team of Shandong Province Higher Education Institutions (Grant No. 1716009), the Special Funds of Taishan Scholar Project (Grant No. tsqn20161041), and the Colleges and Universities Youth Innovation Technology Program of Shandong Province (Grant No. 2019KJI011).
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Zhang, F. Stochastic maximum principle for optimal control problems involving delayed systems. Sci. China Inf. Sci. 64, 119206 (2021). https://doi.org/10.1007/s11432-019-2826-3
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DOI: https://doi.org/10.1007/s11432-019-2826-3