Abstract:

The properties in respect to Z, the second part solution process of a new type anticipated backward stochastic differential equations (anticipated BSDE)  are studied. One sufficient condition is  given under which Z is bounded. We apply our result in finding the explicit form of optimal control in the stochastic control problem with delay.
 

Key words: anticipated backward stochastic differential equation; Malliavin calculus; stochastic optimal control with delay