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

• 成果类型: Article
• 署名作者: Hu, Sang; Obloj, Jan; Zhou, Xun Yu
• 署名单位: The Chinese University of Hong Kong, Shenzhen; University of Oxford; University of Oxford; Columbia University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2022.4414
• 发表日期: 2023
• 页码: 2474-2496
• 关键词: casino gambling; cumulative prospect theory; time inconsistency; randomization; Skorokhod embedding

摘要

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 naive 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 formuch 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 naif never stops loss.