# Linear-quadratic stochastic delayed control and deep learning resolution

arXiv: https://arxiv.org/abs/2102.09851 · HTML: https://mlsanity.com/paper/2102.09851/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2021.

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

- [Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control](https://mlsanity.com/paper/2603.19463/) (2026)

## Abstract (arXiv)

We consider a class of stochastic control problems with a delayed control, both in drift and diffusion, of the type dX t = α t--d (bdt + σdW t). We provide a new characterization of the solution in terms of a set of Riccati partial differential equations. Existence and uniqueness are obtained under a sufficient condition expressed directly as a relation between the horizon T and the quantity d(b/σ) 2. Furthermore, a deep learning scheme is designed and used to illustrate the effect of delay on the Markowitz portfolio allocation problem with execution delay.