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

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. This paper was accepted by Kay Giesecke, finance. Funding: The first author acknowledges support from National Natural Science Foundation of China [Grant 11901494] and Natural Science Foundation of Guangdong Province [Grant 2019A1515011396]. The second author gratefully acknowledges support from the European Union’s Seventh Framework Programme/European Research Council [ERC Starting Grant RobustFinMath 335421]. The third author gratefully acknowledges financial support through start-up grants at both the University of Oxford and Columbia University, as well as through the Oxford–Nie Laboratory for Financial Big Data and the Nie Center for Intelligent Asset Management. Supplemental Material: Data are available at https://doi.org/10.1287/mnsc.2022.4414 .