Paper: arXiv 2610.24558

Authors: Matteo Smerlak

Abstract

The value of a forecast depends on its accuracy, but also on its actionability. In trading, an investor must translate return forecasts into positions while accounting for trading costs and the lingering impact of earlier trades. We solve the stationary quadratic trading problem with transient price impact using tools from prediction theory: Wiener-Hopf factorization gives the optimal policy as the composition of a conditional forecast and an explicit causal linear filter. We recover the Gârleanu-Pedersen aim-portfolio under exponential resilience and derive fractional trading filters under power-law impact decay, requiring memory beyond finite-dimensional LQR control. At fixed positive risk penalty, signals of equal instantaneous predictive strength have equal frictionless Markowitz value. With trading costs, net attainable value is determined by the mean square of the friction-weighted conditional forecast. Under power-law impact with exposure bleeding, we find an intermediate optimal mean-reversion rate for Ornstein-Uhlenbeck signals.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly mathematical and theoretical solution to an optimal trading problem using advanced prediction theory. While the mathematical framework is robust and novel, there is no empirical validation or backtesting presented in the provided excerpt, placing it firmly in the ‘Lab Rats’ quadrant. The clarity is good for the target audience, but reproducibility is moderate due to the theoretical nature and lack of explicit code/data.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Trading Filters & Value of Predictive Signals] --> B{Key Methodology: Wiener-Hopf Factorization & Prediction Theory};
    B --> C[Inputs: Stationary Quadratic Trading Problem, Transient Price Impact];
    C --> D(Computational Processes: Solve Optimal Policy, Derive Filters);
    D --> E[Key Findings: Optimal policy as conditional forecast + causal linear filter; Fractional trading filters; Value determined by friction-weighted conditional forecast; Optimal mean-reversion rate for OU signals];