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Cash-Constrained Multi-Asset Optimal Execution

Article arXiv papers · Author: Ryuji Hashimoto et al.
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Summary

This paper extends the Almgren–Chriss optimal execution framework to account for shared capital limits when rebalancing several assets. It constrains expected cumulative cash spending at every trading period, so a schedule must remain feasible throughout execution rather than only at its endpoint. The authors formulate the problem as a quadratically constrained quadratic program and show that, under mild conditions, it can be represented as a convex optimization problem.

Synthetic experiments indicate that tighter cash limits shift schedules toward selling assets before buying them. In an out-of-sample agent-based market simulation, the method lowers peak cash drawdown while keeping implementation shortfall comparable to existing strategies. The evidence is limited to the reported synthetic and simulated settings; the description does not establish how the framework performs in live markets or across different market conditions.

Key ideas

  • The framework constrains expected cumulative cash use at every execution period.
  • The multi-asset problem can be expressed as a QCQP and convexified under mild conditions.
  • Tighter cash budgets tend to favor schedules that sell before buying.
  • Simulated evaluation reports lower peak cash drawdown with comparable implementation shortfall.

Tags

Multi-assetExecutionRisk management
Full text
# Feasible Multi-Asset Optimal Execution under Cash Constraints


# Feasible Multi-Asset Optimal Execution under Cash Constraints









Optimal execution (OE) in multi-asset settings involves complex interactions across assets, particularly through shared capital constraints during portfolio rebalancing. While existing models capture cross-impact and portfolio-level dynamics, they largely overlook the role of explicit cash constraints along the execution trajectory. As a result, the feasibility of execution strategies under limited capital remains poorly understood. In this paper, we extend the classical Almgren-Chriss framework to incorporate intertemporal constraints on expected cash consumption, requiring that the expected cumulative cash spent does not exceed a prescribed budget at every trading period. We show that the resulting multi-asset OE problem can be equivalently formulated as a quadratically constrained quadratic program (QCQP), and further establish that it admits a convex representation under mild conditions. This provides a tractable framework for analyzing execution strategies under dynamic capital constraints. Through controlled synthetic experiments, we show that the proposed cash constraints qualitatively alter OE schedules toward cash-feasible sell-first executions as the constraints become tighter. Furthermore, evaluations in an out-of-sample agent-based market simulator demonstrate that our method substantially reduces peak cash drawdown while maintaining implementation shortfall comparable to existing execution strategies. Our results highlight the importance of explicitly modeling financial feasibility in multi-asset execution and provide a foundation for bridging theoretical OE models with practical capital constraints.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.