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

SUMMARY 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. Copyright © 2015 John Wiley & Sons, Ltd.

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