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

By Yan Dolinsky

Rating

1864
Battle Count: 56

Relevance

9/10
Highly relevant for high-frequency and medium-frequency trading strategies relying on mean reversion, as it quantifies the severe degradation in performance and potential for infinite loss when using naive projection of full-information strategies under latency.

Implementation Complexity

6/10
The optimal strategy requires solving a linear Volterra equation via forward recursion, which is computationally feasible but more complex than simple threshold rules. The analytical formulas for value are explicit.

Reproducibility

3/5
The paper provides explicit analytical formulas and numerical examples with specified parameters (seed, grid size). While no public code repository is linked, the mathematical derivations and simulation details are fully described, allowing for reproduction by an expert.

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.

Links

arXiv:2610.21447 ยท Paper rankings

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