A MODIFIED METHOD OF SUCCESSIVE APPROXIMATIONS FOR STOCHASTIC RECURSIVE OPTIMAL CONTROL PROBLEMS

摘要

Based on the stochastic maximum principle for the partially coupled forward -backward stochastic control system (FBSCS), a modified method of successive approximations (MSA) is established for stochastic recursive optimal control problems. The second-order adjoint processes are introduced in the augmented Hamiltonian minimization step since the control domain is not necessarily convex. Thanks to the theory of bounded mean oscillation martingales, we give a del-icate proof of the error estimate and then prove the convergence of the modified MSA algorithm. In a special case, we obtain a logarithmic convergence rate. When the control domain is convex and compact, a sufficient condition which makes the control returned from the MSA algorithm be a near-optimal control is given for a class of linear FBSCSs.