Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908910955266048 |
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| author | Ackermann, Julia Kruse, Thomas Urusov, Mikhail |
| author_facet | Ackermann, Julia Kruse, Thomas Urusov, Mikhail |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework Ackermann, Julia Kruse, Thomas Urusov, Mikhail Optimization and Control Probability Mathematical Finance Trading and Market Microstructure 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]. |
| title | Multi-asset optimal trade execution with stochastic cross-effects: An Obizhaeva-Wang-type framework |
| topic | Optimization and Control Probability Mathematical Finance Trading and Market Microstructure |
| url | https://arxiv.org/abs/2503.05594 |