Anticipative stochastic control

The stochastic optimal control problem is solved over the class of anticipative controls. This is done by reducing the stochastic problem to a family of deterministic problems parametrized by ω∈Ω (almost sure optimal control). It is shown that the value function of the anticipative optimal control problem is obtained by averaging over the sample space the unique global solution of a Hamilton-Jacobi-Bellman stochastic partial differential equation. The stochastic characteristics representation of this solution is used to express the cost of perfect information, which is the difference between the cost function of the nonanticipative control problem and the cost of the anticipative control problem