A global stochastic maximum principle for delayed forward-backward stochastic control systems

Abstract

In this paper, we study a delayed forward-backward stochastic control system in which all the coefficients depend on the state and control terms, and the control domain is an arbitrary nonempty set. To handle the terms involving $y$ and $z$ in the second-order expansion, we derive two decompositions of $\big(\hat{y}^\e(\cd), \hat{z}^\e(\cd)\big)$. More precisely, we use the second decomposition to handle the terms involving $f^\e_{yy}, f^\e_{yz}$ and use both decompositions to handle the term involving $f^\e_{zz}$. Finally, a global stochastic maximum principle is obtained.

arXiv commentSubstantial revisions, including corrections to the proofs