Conjugate duality in stochastic controls with delay

Wang, Zimeng; Hodge, David J.; Le, Huiling

Abstract

This paper uses the method of conjugate duality to investigate a class of stochastic optimal control problems where state systems are described by stochastic differential equations with delay. For this, we first analyse a stochastic convex problem with delay and derive the expression for the corresponding dual problem. This enables us to obtain the relationship between the optimalities for the two problems. Then, by linking stochastic optimal control problems with delay with a particular type of stochastic convex problem, the result for the latter leads to sufficient maximum principles for the former.

Citation

Wang, Z., Hodge, D. J., & Le, H. (2017). Conjugate duality in stochastic controls with delay. Advances in Applied Probability, 49(4), https://doi.org/10.1017/apr.2017.32

• Journal Article Type: Article
• Acceptance Date: Jul 6, 2017
• Online Publication Date: Nov 17, 2017
• Publication Date: Dec 1, 2017
• Deposit Date: Jul 20, 2017
• Publicly Available Date: Nov 17, 2017
• Journal: Advances in Applied Probability
• Print ISSN: 0001-8678
• Electronic ISSN: 1475-6064
• Publisher: Applied Probability Trust
• Peer Reviewed: Peer Reviewed
• Volume: 49
• Issue: 4
• DOI: https://doi.org/10.1017/apr.2017.32
• Keywords: Anticipated backward stochastic differential equation; Conjugate convex function; Stochastic delay differential equation; Stochastic maximum principle; Stochastic optimal control with delay
• Public URL: https://nottingham-repository.worktribe.com/output/965120
• Publisher URL: https://www.cambridge.org/core/journals/advances-in-applied-probability/article/conjugate-duality-in-stochastic-controls-with-delay/2FB2F1A9A2D1371B3C0303946D129CE5#
• Contract Date: Jul 20, 2017