Optimal locally absolutely continuous change of measure. finite set of decisions. part ii:optimization problems

This article continues Part I. Optimality conditions are studied for a control problem, where the control choice implies locally absolutely continuous transformation of some initial measure. Attention is focused on the derivation of a stochastic differential equation for the value process which is a non-linear analogue of the inverse Girsanov transformation standing for Bellman's equation. In. particular, application of this equation gives a description of the extreme points of the space of controls. The questions of sufficiency of partial information and equivalent transformations of the optimization problem are also studied