Optimal Relaxed Control for a Decoupled G-FBSDE
研究由G-布朗运动驱动的解耦正倒向随机微分方程系统，通过正则化方法证明非光滑随机最优控制问题中松弛最优控制的存在性。
Abstract In this paper we study a system of decoupled forward-backward stochastic differential equations driven by a G -Brownian motion ( G -FBSDEs) with non-degenerate diffusion. Our objective is to establish the existence of a relaxed optimal control for a non-smooth stochastic optimal control problem. The latter is given in terms of a decoupled G -FBSDE. The cost functional is the solution of the backward stochastic differential equation at the initial time. The key idea to establish existence of a relaxed optimal control is to replace the original control problem by a suitably regularised problem with mollified coefficients, prove the existence of a relaxed control, and then pass to the limit.