Model Predictive Control For Trade Execution¶
Authors: Thomas P. McAuliffe, Samuel Liew, Yuchao Li, Andrey Ushenin, Chihang Wang, Alexandros Tasos, Jack Pearce, Dimitris Tasoulis, Dimitri P. Bertsekas, Theodoros Tsagaris Institutions: Bayforest Technologies (London); Arizona State University; MIT Year: 2026 (April 2026) arXiv: 2603.28898 Categories: q-fin.TR
Plain-language abstract¶
Executing a large client order in a continuous double-auction market means balancing three competing objectives:
- Completion risk — finish inside the window.
- Market impact cost — pushing price against yourself by trading fast.
- Opportunity cost — missing favourable moves by trading slow.
Static schedules like TWAP / VWAP are the industry workhorse but cannot react online to changing liquidity or short-horizon signals. This paper proposes a production-grade MPC (Model Predictive Control) framework that at each decision step solves a fast quadratic program trading off expected cost against deviation from the schedule, with a residual cost term from a base policy (a rollout approximation). On 6 months of NASDAQ Level-3 data, the MPC algorithm reduces schedule shortfall by 40–50% vs spread-crossing benchmarks and materially cuts slippage. Adding predictive price information on top improves results further.
Key contributions¶
- MPC = approximate DP for execution — cast the execution problem as a stochastic discrete-time control problem; at each stage, do one-step lookahead with a learned cost-to-go \(\tilde J_{t+1}\) approximating future stage costs via rollout of a simple base policy. Scales and runs in production time; exact DP is intractable.
- Fast quadratic-program per decision step — trade off expected transaction cost against schedule deviation, with explicit bounds on schedule adherence and variance constraints for direct risk control. Runs fast enough to manage hundreds–thousands of simultaneous orders without stale state.
- Modular, production-oriented design — explicit separation of concerns (single-responsibility components with their own KPIs, per Li et al.'s hierarchical-RL spirit) so forecasting, scheduling, and placement can be improved independently.
- Rich action space — not just market/limit binary; full parameterisation across order types, venues, brokers, ATSs. Interactions can happen at Level-3 granularity.
- Empirically validates against strong baselines — spread-crossing, pure TWAP/VWAP, and industry broker algorithms on NASDAQ L3 data for 6 months.
Method summary¶
Stochastic control formulation¶
- State \(x_t\) = market state (prices, volatility, book features) + order state (filled quantity, schedule residual).
- Control \(u_t\) = vector of child orders (prices, sizes, venues) drawn from feasibility set \(U_t(x_t)\).
- Disturbance \(w_t\) = market-driven uncertainty in fills and future prices.
- Dynamics \(x_{t+1} = f_t(x_t, u_t, w_t)\).
- Objective: minimise \(\mathbb{E}\left[g_T(x_T) + \sum_{t=0}^{T-1} g_t(x_t, u_t, w_t)\right]\).
MPC with rollout¶
\[\tilde u_t \in \arg\min_{u_t \in U_t(x_t)} \mathbb{E}\bigl\{ g_t(x_t, u_t, w_t) + \tilde J_{t+1}\bigl(f_t(x_t, u_t, w_t)\bigr) \bigr\}\]
- Base policy for rollout: a simple, well-understood strategy (e.g., TWAP-tracking spread cross) whose expected residual cost \(\tilde J_{t+1}\) approximates the value function.
- Per-step optimisation is a quadratic program: quadratic in \(u_t\) (convex transaction cost + schedule-deviation penalty), linear + variance constraints.
- Solves in low milliseconds, enabling realistic deployment.
Objectives & constraints¶
| Objective | Control mechanism |
|---|---|
| Schedule adherence | Explicit bounds on cumulative deviation from TWAP/VWAP |
| Cost minimisation | Quadratic penalty on expected spread + impact |
| Risk | Variance constraint on deviation |
| Opportunity | Residual cost from rollout base policy |
Extensions considered¶
- Augmenting \(\tilde J_{t+1}\) with predictive price information further improves performance — demonstrates the framework's plug-in flexibility for alpha signals or microstructure forecasters.
- Multistep MPC lookahead is flagged as future work; the paper uses one-step lookahead + rollout only.
Main results (NASDAQ L3, 6 months)¶
- Schedule shortfall reduced by ≈ 40–50% vs spread-crossing benchmarks.
- Significant improvements in slippage (arrival-price, VWAP, and interval slippage — defined in Section 5.2 of the paper).
- Adding a simple predictive price component on top of the rollout base policy gives a further performance lift.
- The QP per decision step is fast enough for live deployment with realistic order counts.
Relation to prior work¶
| Strand | Paper | Role |
|---|---|---|
| DP for execution | Bertsimas & Lo 1998 | TWAP as DP optimum under linear impact |
| Mean-variance execution | Almgren & Chriss 2001 | Efficient frontier of paths; static |
| Dynamic VWAP | Busetti & Boyd 2005 | LQG stochastic control with revealed-volume uncertainty |
| Limit + market mix | Cartea & Jaimungal 2015 | Passive when ahead, aggressive when behind |
| RL-based | Nevmyvaka et al. 2006 | Q-learning directly on NASDAQ LOB |
| RL mapping to schedule | Hendricks & Wilcox | Action = fraction-of-Almgren-Chriss |
| Price-forecast RL | Moallemi & Wang | DDQN with return-forecast features |
| Hierarchical RL | Li et al. | Macro / meta / micro separation — this paper adopts the spirit |
| Prior MPC | Clinet et al.; Plessen & Bemporad | Earlier MPC framings, less production-oriented |
MPC is acknowledged to be closely related to RL — some of the most reliable RL methods are MPC (per Bertsekas's own RL/MPC textbooks). This paper positions MPC as a pragmatic sweet spot between rigid static schedules and full-stack RL.
Limitations¶
- One-step lookahead only — multistep MPC is left for future work.
- Single market: NASDAQ L3 only; cross-venue / dark-pool / ATS routing is in scope conceptually but not benchmarked.
- Base-policy dependence: the rollout quality depends on the base policy; a poor base policy yields a poor \(\tilde J_{t+1}\) approximation.
- No live trading validation: backtests on simulated orders against 6 months of L3 data — simulator fidelity matters (see reality-gap-lob-simulation for why this is non-trivial).
- No formal regret bound: empirical wins, no theoretical optimality guarantee versus the true DP solution.
Connections¶
- Defines the central execution tradeoff: see optimal-execution for the concept page.
- Builds on the Almgren–Chriss / Bertsimas–Lo / Cartea–Jaimungal lineage of optimal-execution research.
- Complementary to reality-gap-lob-simulation — any serious MPC evaluation needs a simulator that reproduces market impact realistically; combining the two gives a credible offline evaluation stack.
- Impact modelling connects to price-impact and the OFI-based linear impact of price-impact-order-book-events.