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Conjugate duality in stochastic controls with delay

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

Authors

Zimeng Wang pmxzw5@nottingham.ac.uk

David J. Hodge

HUILING LE huiling.le@nottingham.ac.uk
Professor of Probability



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 http://eprints.nottingham.ac.uk/id/eprint/44290
Publisher URL https://www.cambridge.org/core/journals/advances-in-applied-probability/article/conjugate-duality-in-stochastic-controls-with-delay/2FB2F1A9A2D1371B3C0303946D129CE5#
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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