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Conjugate duality in stochastic controls with delay

Part of: Stochastic systems and control Stochastic analysis Topological linear spaces and related structures

Published online by Cambridge University Press:  17 November 2017

Zimeng Wang ,
David J. Hodge  and
Huiling Le
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.
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Abstract

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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.

Keywords

Anticipated backward stochastic differential equationconjugate convex functionstochastic delay differential equationstochastic maximum principlestochastic optimal control with delay

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 46A20: Duality theory 60H07: Stochastic calculus of variations and the Malliavin calculus

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 4 , December 2017 , pp. 1011 - 1036
Copyright
Copyright © Applied Probability Trust 2017 

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