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A Casino Gambling Model Under Cumulative Prospect Theory: Analysis and Algorithm

Author

Listed:
  • Sang Hu

    (School of Data Science, Chinese University of Hong Kong, Shenzhen 518172, China)

  • Jan Obłój

    (Mathematical Institute, Oxford-Man Institute of Quantitative Finance, University of Oxford, Oxford OX2 6ED, United Kingdom; St John’s College, Oxford OX1 3JP, United Kingdom)

  • Xun Yu Zhou

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

Abstract

We develop an approach to solve the Barberis casino gambling model [Barberis N (2012) A model of casino gambling. Management Sci. 58(1):35–51] in which a gambler whose preferences are specified by the cumulative prospect theory (CPT) must decide when to stop gambling by a prescribed deadline. We assume that the gambler can assist their decision using independent randomization. The problem is inherently time inconsistent because of the probability weighting in CPT, and we study both precommitted and naïve stopping strategies. We turn the original problem into a computationally tractable mathematical program from which we devise an algorithm to compute optimal precommitted rules that are randomized and Markovian. The analytical treatment enables us to confirm the economic insights of Barberis for much longer time horizons and to make additional predictions regarding a gambler’s behavior, including that, with randomization, a gambler may enter the casino even when allowed to play only once and that it is prevalent that a naïf never stops loss.

Suggested Citation

  • Sang Hu & Jan Obłój & Xun Yu Zhou, 2023. "A Casino Gambling Model Under Cumulative Prospect Theory: Analysis and Algorithm," Management Science, INFORMS, vol. 69(4), pages 2474-2496, April.
    • Handle: RePEc:inm:ormnsc:v:69:y:2023:i:4:p:2474-2496
    DOI: 10.1287/mnsc.2022.4414
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    References listed on IDEAS

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    3. Rachel Croson & James Sundali, 2005. "The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos," Journal of Risk and Uncertainty, Springer, vol. 30(3), pages 195-209, May.
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    7. Rawley Heimer & Zwetelina Iliewa & Alex Imas & Martin Weber, 2021. "Dynamic Inconsistency in Risky Choice: Evidence From the Lab and Field," CRC TR 224 Discussion Paper Series crctr224_2021_274, University of Bonn and University of Mannheim, Germany.
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    Cited by:

    1. Min Dai & Yu Sun & Zuo Quan Xu & Xun Yu Zhou, 2024. "Learning to Optimally Stop Diffusion Processes, with Financial Applications," Papers 2408.09242, arXiv.org, revised Sep 2024.

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