A Central Limit Theorem, Loss Aversion and Multi-Armed Bandits

Zengjing Chen, Larry G. Epstein, Guodong Zhang

This paper establishes a central limit theorem under the assumption that conditional variances can vary in a largely unstructured history-dependent way across experiments subject only to the restriction that they lie in a fixed interval. Limits take a novel and tractable form, and are expressed in terms of oscillating Brownian motion. A second contribution is application of this result to a class of multi-armed bandit problems where the decision-maker is loss averse.

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