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Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework

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  • Julia Ackermann
  • Thomas Kruse
  • Mikhail Urusov

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].

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  • Julia Ackermann & Thomas Kruse & Mikhail Urusov, 2025. "Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework," Papers 2503.05594, arXiv.org.
    • Handle: RePEc:arx:papers:2503.05594
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    References listed on IDEAS

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