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

Bernt Oksendal 1 Agnès Sulem 2 Tusheng Zhang 3
2 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
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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Bernt Oksendal, Agnès Sulem, Tusheng Zhang. Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations. [Research Report] RR-7518, INRIA. 2011, pp.29. ⟨inria-00560229⟩

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