Long-Horizon Investment with Delayed Information in a Mean-Reverting Market

Paper: arXiv 2610.21447

Authors: Yan Dolinsky

Abstract

We study long-term investment in an Ornstein-Uhlenbeck diffusion model with exponential utility. We solve the finite-horizon problem explicitly and show that information delay qualitatively alters long-horizon behavior. Under full information, the certainty equivalent generated by mean reversion grows quadratically with the investment horizon. With any fixed positive delay, it grows only linearly, at an asymptotic rate that we compute explicitly. We derive an explicit causal representation of the optimal delayed portfolio and show that projecting the full-information strategy onto delayed information can fail dramatically: the resulting exponential loss becomes infinite for sufficiently long horizons. Numerical examples illustrate the economic impact of information delay.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly mathematical and theoretical analysis of investment strategies under delayed information. While the derivations are explicit and detailed, the empirical validation is limited to numerical illustrations rather than extensive backtesting or real-world data analysis. The core contribution lies in the novel analytical solution for the impact of information delay.

Research Flowchart

  flowchart TD
    A[Research Goal: Impact of Delayed Information on Long-Horizon Investment] --> B{Methodology: Ornstein-Uhlenbeck Diffusion Model};
    B --> C[Inputs: Exponential Utility, Mean-Reverting Market (OU Process)];
    C --> D{Computational Process: Explicit Solution of Finite-Horizon Problem};
    D --> E[Outcome 1: Information Delay Qualitatively Alters Long-Horizon Behavior];
    E --> F[Outcome 2: Certainty Equivalent Growth: Quadratic (Full Info) vs. Linear (Delayed Info)];
    F --> G[Outcome 3: Optimal Delayed Portfolio Derived; Naive Projection Fails Dramatically];