Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations

2011/06/01 by Bernt Øksendal, Agnès Sulem, Tusheng Zhang · 1 citation

paper · doi:10.1239/aap/1308662493

crossref issued 2011/06/01 · crossref published 2011/06/01 · crossref published-print 2011/06/01 · crossref created 2011/06/21 · crossref published-online 2016/07/01 · crossref deposited 2019/04/27 · crossref indexed 2026/08/01

Abstract

We study optimal control problems for (time-)delayed stochastic differential equations with jumps. We establish sufficient and necessary stochastic maximum principles for an optimal control of such systems. The associated adjoint processes are shown to satisfy a (time-)advanced backward stochastic differential equation (ABSDE). Several results on existence and uniqueness of such ABSDEs are shown. The results are illustrated by an application to optimal consumption from a cash flow with delay.

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• Anticipated backward stochastic evolution equations and maximum principle for path-dependent systems in infinite dimensions

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