When and what to learn in a changing world

TL;DR

This paper analyzes optimal strategies for acquiring information over time in a changing environment, revealing when to learn and how information patterns evolve, with applications to portfolio management.

Contribution

It introduces a decomposition of the dynamic decision problem into optimal stopping and static information acquisition, providing a clear characterization of long-term learning policies.

Findings

Optimal policies involve stopping or cyclic information updates.

As fixed costs vanish, belief updates become lumped, leading to waiting or confirmation strategies.

Long run dynamics are characterized by the 'virtual flow payoff'.

Abstract

A decision-maker periodically acquires information about a changing state, controlling both the timing and content of updates. I characterize optimal policies using a decomposition of the dynamic problem into optimal stopping and static information acquisition. Eventually, information acquisition either stops or follows a simple cycle in which updates occur at regular intervals to restore prescribed levels of relative certainty. This enables precise analysis of long run dynamics across environments. As fixed costs of information vanish, belief changes become lumpy: it is optimal to either wait or acquire information so as to exactly confirm the current belief until rare news prompts a sudden change. The long run solution admits a closed-form characterization in terms of the "virtual flow payoff". I highlight an illustrative application to portfolio diversification.