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Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model

Author

Listed:
  • Xue Dong He

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong)

  • Sang Hu

    (School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China)

  • Jan Obłój

    (Mathematical Institute, Oxford-Man Institute of Quantitative Finance and St John’s College, University of Oxford, Oxford OX2 6GG, United Kingdom)

  • Xun Yu Zhou

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

Abstract

We consider the dynamic casino gambling model initially proposed by Barberis (2012) and study the optimal stopping strategy of a precommitting gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis (2012) [Barberis N (2012) A model of casino gambling. Management Sci. 58(1): 35–51.] can be strictly improved by reviewing the betting history or by tossing an independent coin, and we explain that the improvement generated by using randomized strategies results from the lack of quasi-convexity of CPT preferences. Moreover, we show that any path-dependent strategy is equivalent to a randomization of path-independent strategies.

Suggested Citation

  • Xue Dong He & Sang Hu & Jan Obłój & Xun Yu Zhou, 2017. "Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model," Operations Research, INFORMS, vol. 65(1), pages 97-103, February.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:1:p:97-103
    DOI: 10.1287/opre.2016.1545
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    References listed on IDEAS

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