Optimal Portfolio Choice with Cross-Impact Propagators

Fuente: arXiv
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Main Authors: Jaber, Eduardo Abi, Neuman, Eyal, Tuschmann, Sturmius
Format: Preprint
Published: 2024
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author Jaber, Eduardo Abi
Neuman, Eyal
Tuschmann, Sturmius
author_facet Jaber, Eduardo Abi
Neuman, Eyal
Tuschmann, Sturmius
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_10273
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Optimal Portfolio Choice with Cross-Impact Propagators
Jaber, Eduardo Abi
Neuman, Eyal
Tuschmann, Sturmius
Portfolio Management
Mathematical Finance
Trading and Market Microstructure
93E20, 60H30, 91G80
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.
title Optimal Portfolio Choice with Cross-Impact Propagators
topic Portfolio Management
Mathematical Finance
Trading and Market Microstructure
93E20, 60H30, 91G80
url https://arxiv.org/abs/2403.10273