Optimal Portfolio Choice with Cross-Impact Propagators

TL;DR

This paper develops an explicit solution framework for optimal portfolio selection in continuous time considering complex cross-impact effects, providing insights into how impact propagators influence trading strategies and market manipulation.

Contribution

It introduces a novel explicit solution to portfolio optimization with matrix-valued Volterra propagators and establishes conditions preventing price manipulation.

Findings

Explicit solutions via operator resolvents for portfolio optimization.

Conditions ensuring no price manipulation with cross-impact.

Insights into impact effects on optimal trading strategies.

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.