Optimal control of backward doubly stochastic system

Mean-field anticipated BSDEs driven by time-changed Lévy noises

“…Using the duality, they solved some stochastic optimal control problems (see e.g. Xu [20], Yu [21], Giulia and Steffen [7], Klimsiak [9], Wang [19], Wang, Shi and Meng [18], Zhang and Yan [22], among others).…”

Necessary condition for optimal control of doubly stochastic systems

“…A similar work can be seen in Ji, Wei and Zhang [18] and Bahlali, Gherbal [8] for convex control domains (see references for more details). Subsequently, Wang and Liu [38,39] established the necessary conditions for only backward doubly stochastic control system, via the second-order Taylor expansion under no restriction on the convexity of control domain and the diffusion coefficient does not contain the control variable. However, as the authors claimed in their papers, necessary condition (22) or (26) is not very perfect.…”