Optimal Trade Execution

Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework ArXiv ID: 2503.05594 “View on arXiv” Authors: Unknown Abstract We analyze a continuous-time optimal trade execution problem in multiple assets where the price impact and the resilience can be matrix-valued stochastic processes that incorporate cross-impact effects. In addition, we allow for stochastic terminal and running targets. Initially, we formulate the optimal trade execution task as a stochastic control problem with a finite-variation control process that acts as an integrator both in the state dynamics and in the cost functional. We then extend this problem continuously to a stochastic control problem with progressively measurable controls. By identifying this extended problem as equivalent to a certain linear-quadratic stochastic control problem, we can use established results in linear-quadratic stochastic control to solve the extended problem. This work generalizes [“Ackermann, Kruse, Urusov; FinancStoch'24”] from the single-asset setting to the multi-asset case. In particular, we reveal cross-hedging effects, showing that it can be optimal to trade in an asset despite having no initial position. Moreover, as a subsetting we discuss a multi-asset variant of the model in [“Obizhaeva, Wang; JFinancMark'13”]. ...

Residual U-net with Self-Attention to Solve Multi-Agent Time-Consistent Optimal Trade Execution ArXiv ID: 2312.09353 “View on arXiv” Authors: Unknown Abstract 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 to a backward stochastic differential equation (BSDE) to extend the problem to multiple agents and assets. We utilize a residual U-net with self-attention to numerically approximate the value function for multiple agents and assets which can be used to determine the time-consistent optimal control. In this paper, we show that the proposed neural network approach overcomes the limitations of finite difference methods. We validate our results and study parameter sensitivity. With our framework we study how an agent with significant price impact interacts with an agent without any price impact and the optimal strategies used by both types of agents. We also study the performance of multiple sellers and buyers and how they compare to a holding strategy under different economic conditions. ...