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