Search Results for « Optimal Execution »

We show that optimal execution under nonlinear transient market impact can be represented as a transformer sequence model. The propagator becomes causal attention; the execution strategy's cost becomes the forward pass through a neural network. This opens up the possibility of using a neural-network-optimized stack, such as PyTorch and the Adam optimizer on Nvidia GPUs, to compute optimal trading paths in the propagator model, as well as to train model parameters from realized executions of metaorders. For power-law impact and decay, our method matches or improves on the table of optimal values reported by Curato, Gatheral, and Lillo (2017), and on signed schedules reaches those values significantly faster than the sequential quadratic programming method. A single batched descent allows us to map signed-acquisition costs together with round-trip manipulation certificates across a plane parameterized by the impact and propagator exponents. A similar batched computation locates the slippage frontier at a manipulable exponent pair, where slippage renders the signed execution problem well posed.

We study deterministic optimal execution strategies under the continuous time variant of the permanent/temporary impact cost framework of Almgren-Chriss [AC] with arrival price benchmark and the transient impact cost framework of Gatheral [G] with volume weighted average price benchmark. For Almgren-Chriss framework we assume non-linear permanent/temporary impact costs and characterize optimal strategies using variational methods, and distinguish full-horizon liquidation, early completion, and regimes of non-attainment. For Gatheral framework we assume linear transient impact cost with exponential or power-law decay kernel, deterministic polynomial market volume, constant volatility, and derive explicit solutions.

This paper develops a comprehensive stochastic control framework for optimal execution that systematically incorporates self-exciting order flow dynamics through Hawkes processes. While classical execution models like Almgren-Chriss and Obizhaeva-Wang provide foundational insights, they fail to capture the clustered order flow patterns empirically observed in modern electronic markets. Our framework bridges this gap by embedding multivariate Hawkes processes within a transient price impact model, yielding adaptive execution strategies that respond intelligently to market microstructure conditions. Theoretical contributions include the derivation of closed-form optimal policies under exponential kernel specifications, the establishment of rigorous viability conditions that prevent price manipulation, and the development of a Markovian representation that maintains tractability while approximating power-law decay patterns through complete monotone mixtures. The resulting Hawkes-LQ controller decomposes optimally into baseline, trend-following, and dynamic components, providing both mathematical rigor and economic intuition. Empirical analysis demonstrates economically significant and statistically robust improvements over classical benchmarks. Across extensive Monte Carlo simulations and empirical validation on equity data, the Hawkes-LQ strategy achieves cost reductions of 7.8%-15.8% versus industry standards, with particularly strong performance in the medium-to-high clustering regimes empirically observed across major stocks. Beyond cost reduction, the framework provides superior risk management characteristics, including 14.6% lower Value-at-Risk and more predictable execution outcomes. The framework maintains practical implementability with computational requirements suitable for real-time deployment and demonstrates remarkable robustness to model misspecification. Our work provides both a theoretical foundation and practical methodology for the next generation of execution algorithms, addressing the critical need for strategies that adapt to the self-exciting nature of modern financial markets.

We derive a mesoscopic model for optimal execution with limit orders that incorporates microstructural features of passive price impact. Our framework is based on two empirical observables: the approximately exponential decay of limit-order fill probabilities with distance from the midprice, and the short-term linear response of price changes to order flow imbalance. Combining these ingredients, we obtain a reduced-form passive impact rate that decays exponentially with quote distance. The model describes passive execution at a tactical level, where fills arise from a sequence of quote adjustments that balance execution probability, adverse selection, and opportunity cost. We formulate and solve an optimal liquidation problem in which the trader controls the aggressiveness of passive sell quotes. This generates a trade-off between higher fill intensity and larger accumulated impact on the one hand, and lower impact but greater non-execution risk on the other. Empirical calibration using NASDAQ equities and public FX supports the empirical foundations of the model. We also analyse extensions with heterogeneous decay rates, transient impact, and target execution schedules.

Abstract Novel technologies allow cryptocurrency exchanges to offer innovative services that set them apart from other exchanges. In this paper we study the distinct features of cryptocurrency fee schedules and the implications for optimal trade execution. We formulate an optimal execution strategy that minimizes the trading fees charged by the exchange. We further provide a proof for the existence of an optimal execution strategy for this type of fee schedule. In fact, the optimal strategy involves both market and limit orders on various price levels. The optimal order distribution scheme depends on the market conditions expressed in terms of the distribution of limit order execution probabilities and the exchange's specific configuration of the fee schedule. Our results indicate that a strategy kernel with an exponentially decaying allocation of trade volume to price levels further away from the best price provides a superior performance and potential reduction of trade execution cost of more than 60%. The robustness of these results is confirmed in an empirical study. To our knowledge this is the first study of optimal trade execution that takes into consideration the full fee schedule of exchanges in general.

We study the quadratic tracking problem of a general stochastic target process with absolutely continuous controls, with and without terminal constraint. We derive explicit, non-asymptotic upper bounds in terms of a Besov-type modulus of the target. These bounds yield sharp explicit rates that specialize to the square-root order for semimartingale targets. We then apply these results to a generalized Obizhaeva–Wang execution model with random terminal inventory. We first develop a Hilbert-space approach to characterize its optimal strategy, which includes jumps. To avoid such trading spikes, one regularizes the problem by a quadratic trading-rate penalty with coefficient ε. We then show that the regularized optimal execution cost—and therefore the excess price impact cost of the regularized optimal strategy—converges at the sharp rate O(√ ε). Since the regularized optimal strategy is not available in closed form, we further construct a nearly optimal strategy which is readily implementable and shares the same approximation rate.

In this paper, we study the optimal execution problem by considering the trading signal and the transaction risk simultaneously. We propose an optimal execution problem by taking into account the trading signal and the execution risk with the associated decay kernel function and the transient price impact function being of generalized forms. In particular, we solve the stochastic optimal control problems under the assumptions that the decay kernel function is the Dirac function and the transient price function is a linear function. We give the optimal executing strategies in state-feedback form and the Hamilton‐Jacobi‐Bellman equations that the corresponding value functions satisfy in the cases of a constant execution risk and a linear execution risk. We also demonstrate that our results can recover previous results when the process of the trading signal degenerates.

Optimal execution in continuously traded digital-asset markets is difficult because a learned policy must react to short-horizon market conditions while still guaranteeing sufficient progress toward a hard terminal inventory target. Standard deep reinforcement learning (DRL) can discover opportunistic schedules, but unconstrained actions can under-trade during low-liquidity intervals and leave large residual inventory for forced terminal liquidation. This paper introduces Forward-Liquidity-Projected Double Deep Q-Learning (FLP-DDQN), a concrete execution algorithm that augments a Double DQN policy with a state-dependent projection layer derived from conservative forward liquidity. The policy selects a multiplier of the urgency baseline, while the projection computes a minimum executable request needed to keep the remaining inventory compatible with forecast future capacity and expands the local upper bound when necessary so that the action interval is non-empty. The method is evaluated on 527,040 consecutive one-minute BTCUSDT Binance Spot observations from calendar year 2024. We construct 5,112 training episodes, 720 validation episodes, and 2,207 strictly out-of-sample hourly execution tasks covering October-December 2024. Across three random seeds, FLP-DDQN achieves a mean implementation shortfall of 3.899 bps versus 4.526 bps for TWAP and 5.507 bps for an otherwise matched DDQN. The episodepaired improvement over TWAP is 0.627 bps with a 95% bootstrap confidence interval of [0.046, 1.593] bps and a one-sided Wilcoxon p-value of 3.94 × 10-26. The matched DDQN ablation shows that the forward-liquidity projection reduces mean shortfall by 1.608 bps and terminal liquidity-breach incidence from 64.9% to 34.6%. Regime tests, random-seed analysis, participation-cap stress, impact stress, and distributional-RL baselines confirm that the principal gain comes from explicit inventory-feasibility control rather than a larger value network.