Optimal Liquidation with Signals: the General Propagator Case
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912588035522560 |
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| author | Jaber, Eduardo Abi Neuman, Eyal |
| author_facet | Jaber, Eduardo Abi Neuman, Eyal |
| contents | We consider a class of optimal liquidation problems where the agent's transactions create transient price impact driven by a Volterra-type propagator along with temporary price impact. We formulate these problems as maximization of a revenue-risk functionals, where the agent also exploits available information on a progressively measurable price predicting signal. By using an infinite dimensional stochastic control approach, we characterize the value function in terms of a solution to a free-boundary $L^2$-valued backward stochastic differential equation and an operator-valued Riccati equation. We then derive analytic solutions to these equations which yields an explicit expression for the optimal trading strategy. We show that our formulas can be implemented in a straightforward and efficient way for a large class of price impact kernels with possible singularities such as the power-law kernel. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_00447 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal Liquidation with Signals: the General Propagator Case Jaber, Eduardo Abi Neuman, Eyal Trading and Market Microstructure Probability 93E20, 60H30, 91G80 We consider a class of optimal liquidation problems where the agent's transactions create transient price impact driven by a Volterra-type propagator along with temporary price impact. We formulate these problems as maximization of a revenue-risk functionals, where the agent also exploits available information on a progressively measurable price predicting signal. By using an infinite dimensional stochastic control approach, we characterize the value function in terms of a solution to a free-boundary $L^2$-valued backward stochastic differential equation and an operator-valued Riccati equation. We then derive analytic solutions to these equations which yields an explicit expression for the optimal trading strategy. We show that our formulas can be implemented in a straightforward and efficient way for a large class of price impact kernels with possible singularities such as the power-law kernel. |
| title | Optimal Liquidation with Signals: the General Propagator Case |
| topic | Trading and Market Microstructure Probability 93E20, 60H30, 91G80 |
| url | https://arxiv.org/abs/2211.00447 |