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”].

Keywords: optimal trade execution, multi-asset trading, stochastic control, price impact, cross-impact

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly theoretical, relying on advanced stochastic calculus, linear-quadratic stochastic control, and backward stochastic differential equations to derive optimal execution strategies, resulting in a high math complexity score. However, it lacks any empirical validation, backtesting, or data-driven implementation, focusing solely on theoretical modeling and continuous-time solutions, leading to a very low empirical rigor score.
  flowchart TD
    A["Research Goal:<br>Generalize Obizhaeva-Wang model<br>to multi-asset with stochastic impacts"] --> B["Method: Stochastic Control Formulation"]
    B --> C["Data: Matrix-valued stochastic<br>processes for impact/resilience"]
    C --> D["Computation: Extend to<br>LQ Stochastic Control"]
    D --> E["Outcome: Closed-form solution<br>identifies cross-hedging effects"]
    E --> F["Outcome: Validation of<br>optimal trading in zero-position assets"]