IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2210.08077.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2210.08077
    File Function: Latest version
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dipankar Mondal & N. Selvaraju, 2022. "Convexity, two-fund separation and asset ranking in a mean-LPM portfolio selection framework," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 225-248, March.
    2. Zengjing Chen & Huaijin Liang & Wei Wang & Xiaodong Yan, 2022. "Long bet will lose: demystifying seemingly fair gambling via two-armed Futurity bandit," Papers 2212.11766, arXiv.org.
    3. Jose Fernandes & Augusto Hasman & Juan Ignacio Pena, 2007. "Risk premium: insights over the threshold," Applied Financial Economics, Taylor & Francis Journals, vol. 18(1), pages 41-59.
    4. Galagedera, Don U.A., 2007. "An alternative perspective on the relationship between downside beta and CAPM beta," Emerging Markets Review, Elsevier, vol. 8(1), pages 4-19, March.
    5. Xingyu Dai & Dongna Zhang & Chi Keung Marco Lau & Qunwei Wang, 2023. "Multiobjective portfolio optimization: Forecasting and evaluation under investment horizon heterogeneity," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(8), pages 2167-2196, December.
    6. Baule, Rainer & Korn, Olaf & Kuntz, Laura-Chloé, 2019. "Markowitz with regret," Journal of Economic Dynamics and Control, Elsevier, vol. 103(C), pages 1-24.
    7. 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).
    8. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    9. Sana Hussain, 2020. "Good volatility vs. bad volatility: The asymmetric impact of financial depth on macroeconomic volatility," Manchester School, University of Manchester, vol. 88(3), pages 405-438, June.
    10. Galagedera, Don U.A. & Brooks, Robert D., 2007. "Is co-skewness a better measure of risk in the downside than downside beta?: Evidence in emerging market data," Journal of Multinational Financial Management, Elsevier, vol. 17(3), pages 214-230, July.
    11. Asgar Ali & K. N. Badhani, 2023. "Downside risk matters once the lottery effect is controlled: explaining risk–return relationship in the Indian equity market," Journal of Asset Management, Palgrave Macmillan, vol. 24(1), pages 27-43, February.
    12. Rongju Zhang & Nicolas Langrené & Yu Tian & Zili Zhu & Fima Klebaner & Kais Hamza, 2019. "Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method," Post-Print hal-02909342, HAL.
    13. Rutkowska-Ziarko, Anna & Markowski, Lesław & Pyke, Christopher & Amin, Saqib, 2022. "Conventional and downside CAPM: The case of London stock exchange," Global Finance Journal, Elsevier, vol. 54(C).
    14. Xie, Nan & Wang, Zongrun & Chen, Sicen & Gong, Xu, 2019. "Forecasting downside risk in China’s stock market based on high-frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 530-541.
    15. Courtney Droms Hatch & Kurt Carlson & William G. Droms, 2018. "Effects of market returns and market volatility on investor risk tolerance," Journal of Financial Services Marketing, Palgrave Macmillan, vol. 23(2), pages 77-90, June.
    16. Ping Cheng, 2004. "Asymmetric Risk Measures and Real Estate Returns," The Journal of Real Estate Finance and Economics, Springer, vol. 30(1), pages 89-102, October.
    17. Mohammad Enamul Hoque & Soo-Wah Low, 2020. "Industry Risk Factors and Stock Returns of Malaysian Oil and Gas Industry: A New Look with Mean Semi-Variance Asset Pricing Framework," Mathematics, MDPI, vol. 8(10), pages 1-28, October.
    18. Anna Rutkowska-Ziarko & Christopher Pyke, 2018. "Wykorzystanie informacji księgowych w analizie ryzyka," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 49, pages 547-554.
    19. Cumova, Denisa & Nawrocki, David, 2014. "Portfolio optimization in an upside potential and downside risk framework," Journal of Economics and Business, Elsevier, vol. 71(C), pages 68-89.
    20. Shushi, Tomer & Yao, Jing, 2020. "Multivariate risk measures based on conditional expectation and systemic risk for Exponential Dispersion Models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 178-186.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2210.08077. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.