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

By Bernt Øksendal, Agnès Sulem, Tusheng Zhang. Advances in Applied Probability, 2011

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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.

Subfields: Control and Systems Engineering, Economics and Econometrics, Finance

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