Optimal Portfolio Choice with Cross-Impact Propagators

ArXiv ID: 2403.10273 “View on arXiv”

Authors: Unknown

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.

Keywords: Optimal Execution, Market Impact, Cross-impact, Stochastic Control, Portfolio Choice

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper presents advanced continuous-time stochastic control theory involving Volterra propagators, operator resolvents, and stochastic Fredholm equations, indicating very high mathematical density. However, while it mentions a numerical study and implementation, the core content focuses on theoretical derivations and sufficient conditions without providing backtests, code, or empirical datasets, placing it in the Lab Rats quadrant.
  flowchart TD
    A["Research Goal:<br>Optimal Portfolio Choice with<br>Cross-Impact Propagators"] --> B["Mathematical Formulation:<br>Maximize Revenue-Risk Functional<br>with Volterra Propagators"]
    B --> C["Solution Method:<br>Operator Resolvents &<br>Stochastic Fredholm Equations"]
    C --> D["Computational Process:<br>Numerical Implementation<br>of Optimal Strategies"]
    D --> E["Outcomes:<br>1. Optimal Portfolio/Execution Strategies<br>2. Conditions for No Price Manipulation<br>3. Insights on Cross-Impact & Alpha Decays"]
    subgraph Data Inputs
        F["Key Inputs:<br>Matrix Propagators, Price Signals,<br>Risk Parameters"]
    end
    F --> B