| Abstract: |
| In this talk we deal with stochastic optimal control problems with delay in the state, and we focus on the Pontryagin Maximum principle. It is well known that when we consider a controlled delay state equation, the adjoint BSDE turns out to be anticipating, see [1].
\newline We introduce a new class of anticipating BSDEs suitable to treat general control problems with delay in the state via the stochastic maximum principle.
\newline We show how to handle delay in the control variable.
\newline Next we discuss possible approaches to formulate the stochastic maximum principle for controlled delay equations with control-dependent-noise when the space of controls is not convex.
\newline Part of the talk is based on [2], and on a joint work in progress with G. Guatteri.
[1] Peng, S. Yang, Z., Anticipated backward stochastic differential equations, {\em Ann. Probab.}, 37, 877-902, (2009)
[2] Guatteri, G., Masiero, F., Orrieri, Stochastic maximum principle for SPDEs with delay, {\em Stochastic Process. Appl.}, 127 (2017), no. 7, pp. 2396-2427. } |
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