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Optimal Portfolio Choice with Cross-Impact Propagators

Author

Listed:
  • Eduardo Abi Jaber

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Eyal Neuman

    (Imperial College London)

  • Sturmius Tuschmann

    (Imperial College London)

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," Working Papers hal-04567802, HAL.
    • Handle: RePEc:hal:wpaper:hal-04567802
    Note: View the original document on HAL open archive server: https://hal.science/hal-04567802
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