Maximum principle for optimal control of anticipated forward–backward stochastic differential delayed systems with regime switching |
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Authors: | Siyu Lv Ran Tao Zhen Wu |
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Affiliation: | School of Mathematics, Shandong University, Jinan, China |
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Abstract: | 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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Keywords: | forward– backward stochastic system maximum principle regime switching Markov chain stochastic differential equation with delay anticipated backward stochastic differential equation |
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