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Approximate optimality and the risk/reward tradeoff in a class of bandit problems

Author

Listed:
  • Zengjing Chen

    (Shandong University)

  • Larry G. Epstein

    (McGill University)

  • Guodong Zhang

    (Shandong University)

Abstract

This paper studies a sequential decision problem where payoff distributions are known and where the riskiness of payoffs matters. Equivalently, it studies sequential choice from a repeated set of independent lotteries. The decision-maker is assumed to pursue strategies that are approximately optimal for large horizons. By exploiting the tractability afforded by asymptotics, conditions are derived characterizing when specialization in one action or lottery throughout is asymptotically optimal and when optimality requires intertemporal diversification. The key is the constancy or variability of risk attitude. The main technical tool is a new central limit theorem.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2210.08077
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    References listed on IDEAS

    as
    1. 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).
    2. Fima Klebaner & Zinoviy Landsman & Udi Makov & Jing Yao, 2017. "Optimal portfolios with downside risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 315-325, March.
    3. Chen, Zengjing & Epstein, Larry G., 2022. "A central limit theorem for sets of probability measures," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 424-451.
    4. Nantell, Timothy J. & Price, Barbara, 1979. "An Analytical Comparison of Variance and Semivariance Capital Market Theories," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 14(2), pages 221-242, June.
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