# Existence of an Optimal Control for a coupled FBSDE with a non degenerate diffusion coefficient

arXiv: https://arxiv.org/abs/1702.00194 · HTML: https://mlsanity.com/paper/1702.00194/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2017.

## Built on by (most cited first, 1 of 1)

- [A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs](https://mlsanity.com/paper/2204.05796/) (2022)

## Abstract (arXiv)

We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential equation (BSDE), at the initial time. Our goal is to find an optimal control which minimizes the cost functional. The method consists to construct a sequence of approximating controlled systems for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we establish the existence of a relaxed optimal control to the initial problem. The existence of a strict control follows from the Filippov convexity condition. Our results improve in some sense those of Buckdahn et al..