Anticipated BSDEs driven by time-changed Lévy noises

In this paper, we discuss a class of anticipated backward stochastic differential equations (anticipated BSDEs, in short) driven by time-changed Lévy noises. We establish the existence and uniqueness of the solution. Moreover, we establish the duality relation between stochastic differential delay equations (SDDEs, in short) and anticipated BSDEs driven by time-changed Lévy noises.