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Mathematics > Optimization and Control

arXiv:1812.11283 (math)
[Submitted on 29 Dec 2018]

Title:Maximum principle for stochastic optimal control problem of forward-backward stochastic difference systems

Authors:Shaolin Ji, Haodong Liu
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Abstract:In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss). Two types of FBS{\Delta}Ss are investigated. The first one is described by a partially coupled forward-backward stochastic difference equation (FBS{\Delta}E) and the second one is described by a fully coupled FBS{\Delta}E. By adopting an appropriate representation of the product rule and an appropriate formulation of the backward stochastic difference equation (BS{\Delta}E), we deduce the adjoint difference equation. Finally, the maximum principle for this optimal control problem with the control domain being convex is established.
Comments: 24 pages
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1812.11283 [math.OC]
  (or arXiv:1812.11283v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.11283

Submission history

From: Shaolin Ji [view email]
[v1] Sat, 29 Dec 2018 04:26:04 UTC (20 KB)
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