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

Lv Siyu | Zendy; Tao Ran | Zendy; Wu Zhen | Zendy

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

Author(s) -

Lv Siyu,

Tao Ran,

Wu Zhen

Publication year - 2015

Publication title -

optimal control applications and methods

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.458

H-Index - 44

eISSN - 1099-1514

pISSN - 0143-2087

DOI - 10.1002/oca.2160

Subject(s) - maximum principle , optimal control , pontryagin's minimum principle , markov chain , stochastic differential equation , duality (order theory) , mathematics , stochastic control , mathematical optimization , state (computer science) , differential (mechanical device) , regular polygon , consumption (sociology) , control (management) , mathematical economics , control theory (sociology) , computer science , discrete mathematics , algorithm , social science , sociology , statistics , geometry , artificial intelligence , engineering , aerospace engineering

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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