Residual U-net with Self-Attention to Solve Multi-Agent Time-Consistent Optimal Trade Execution

In this paper, we explore the use of a deep residual U-net with self-attention to solve the the continuous time time-consistent mean variance optimal trade execution problem for multiple agents and assets. Given a finite horizon we formulate the time-consistent mean-variance optimal trade execution problem following the Almgren-Chriss model as a Hamilton-Jacobi-Bellman (HJB) equation. The HJB formulation is known to have a viscosity solution to the unknown value function. We reformulate the HJB ...