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A central limit theorem, loss aversion and multi-armed bandits

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  • Chen, Zengjing
  • Epstein, Larry G.
  • Zhang, Guodong

Abstract

This paper studies a multi-armed bandit problem where the decision-maker is loss averse, in particular she is risk averse in the domain of gains and risk loving in the domain of losses. The focus is on large horizons. Consequences of loss aversion for asymptotic (large horizon) properties are derived in a number of analytical results. The analysis is based on a new central limit theorem for a set of measures under which conditional variances can vary in a largely unstructured history-dependent way subject only to the restriction that they lie in a fixed interval.

Suggested Citation

  • Chen, Zengjing & Epstein, Larry G. & Zhang, Guodong, 2023. "A central limit theorem, loss aversion and multi-armed bandits," Journal of Economic Theory, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:jetheo:v:209:y:2023:i:c:s0022053123000418
    DOI: 10.1016/j.jet.2023.105645
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    Cited by:

    1. Zengjing Chen & Larry G. Epstein & Guodong Zhang, 2022. "Approximate optimality and the risk/reward tradeoff in a class of bandit problems," Papers 2210.08077, arXiv.org, revised Dec 2023.
    2. Vladimir V. Ulyanov, 2024. "From Classical to Modern Nonlinear Central Limit Theorems," Mathematics, MDPI, vol. 12(14), pages 1-17, July.

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    More about this item

    Keywords

    Multi-armed bandit; Loss aversion; Sequential sampling; Large-horizon approximations; Central limit theorem; Oscillating Brownian motion;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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