Maximum principle for optimal control of anticipated forward‐backward stochastic differential delayed systems with regime switching

This paper is concerned with a Pontryagin maximum principle for optimal control problem of stochastic system, which is described by an anticipated forward–backward stochastic differential delayed equation and modulated by a continuous‐time finite‐state Markov chain. We establish a necessary maximum principle and sufficient verification theorem for the optimal control by virtue of the duality method and convex analysis. To illustrate the theoretical results, we apply them to a recursive utility investment‐consumption problem, and the optimal consumption rate is derived explicitly.