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Optimal Portfolio Choice with Cross-Impact Propagators

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  • Eduardo Abi Jaber
  • Eyal Neuman
  • Sturmius Tuschmann

Abstract

We consider a class of optimal portfolio choice problems in continuous time where the agent's transactions create both transient cross-impact driven by a matrix-valued Volterra propagator, as well as temporary price impact. We formulate this problem as the maximization of a revenue-risk functional, where the agent also exploits available information on a progressively measurable price predicting signal. We solve the maximization problem explicitly in terms of operator resolvents, by reducing the corresponding first order condition to a coupled system of stochastic Fredholm equations of the second kind and deriving its solution. We then give sufficient conditions on the matrix-valued propagator so that the model does not permit price manipulation. We also provide an implementation of the solutions to the optimal portfolio choice problem and to the associated optimal execution problem. Our solutions yield financial insights on the influence of cross-impact on the optimal strategies and its interplay with alpha decays.

Suggested Citation

  • Eduardo Abi Jaber & Eyal Neuman & Sturmius Tuschmann, 2024. "Optimal Portfolio Choice with Cross-Impact Propagators," Papers 2403.10273, arXiv.org.
    • Handle: RePEc:arx:papers:2403.10273
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    References listed on IDEAS

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    1. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2022. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Post-Print hal-02567489, HAL.
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    5. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Papers 2004.01624, arXiv.org, revised Mar 2022.
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