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Approximate optimality and the risk/reward tradeoff given repeated gambles

Author

Listed:
  • Zengjing Chen

    (Shandong University
    Shandong National Center for Applied Mathematics)

  • 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, that is, the decision-maker’s risk/reward tradeoff.

Suggested Citation

  • Zengjing Chen & Larry G. Epstein & Guodong Zhang, 2025. "Approximate optimality and the risk/reward tradeoff given repeated gambles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(4), pages 1351-1381, June.
    • Handle: RePEc:spr:joecth:v:79:y:2025:i:4:d:10.1007_s00199-024-01614-4
    DOI: 10.1007/s00199-024-01614-4
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    More about this item

    Keywords

    Risk/reward tradeoff; Large-horizon approximations; Central limit theorem; Repeated gambles; Diversification; Multi-armed bandit;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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