Optimal control of a stochastic diffusion process with functional equality and inequality constraints

Abstract

We consider a problem of optimal control of a multidimensional process specified by Ito stochastic differential equation, in the presence of functional equality and inequality constraints on the phase trajectory, with the control acting on the drift coefficient. Sufficiently general and at the same time constructively verifiable first- and second-order necessary optimality conditions are formulated in terms of variations of functionals.