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

Sang Hu (), Jan Obłój () and Xun Yu Zhou ()
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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

Management Science, 2023, vol. 69, issue 4, 2474-2496

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.

Keywords: casino gambling; cumulative prospect theory; time inconsistency; randomization; Skorokhod embedding (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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