A maximum principle for controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints

Shaolin Ji, Qingmeng Wei, Xiumin Zhang

Published 2010-05-18, updated 2012-11-17Version 2

In this paper, we study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints. Applying the terminal perturbation method and Ekeland's variation principle, a necessary condition of the stochastic optimal control, i.e., stochastic maximum principle is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.