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Conjugate duality in stochastic controls with delay

Published online by Cambridge University Press:  17 November 2017

Zimeng Wang*
Affiliation:
University of Nottingham
David J. Hodge*
Affiliation:
University of Nottingham
Huiling Le*
Affiliation:
University of Nottingham
*
* Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
* Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
* Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.

Abstract

In this paper we use 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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2017 

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