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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.