Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation

摘要

This paper first makes an attempt to investigate the near-optimal control of systemsgoverned by fully nonlinear coupled forward-backward stochastic differential equations(FBSDEs) under the assumption of a convex control domain. By Ekeland’s variationalprinciple and some basic estimates for state processes and adjoint processes, we establishthe necessary conditions for anyε-near optimal control in a local form with an error order of exactε1/2. Moreover, under additional convexity conditions on Hamiltonian function, weprove that anε-maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality of orderε1/2.