THE OPTIMAL-CONTROL OF DIFFUSIONS

Using a differentiation result of Blagovescenskii and Freidlin calculations of Bensoussan are simplified and the adjoint process identified in a stochastic control problem in which the control enters both the drift and diffusion coefficients. A martingale representation result of Elliott and Kohlmann is then used to obtain the integrand in a stochastic integral, and explicit forward and backward equations satisfied by the adjoint process are derived. © 1990 Springer-Verlag New York Inc.