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

被引：3

作者：

Hu, Sang ^{[1
]}

Obloj, Jan ^{[2
,3
]}

Zhou, Xun Yu ^{[4
]}

机构：

[1] Chinese Univ Hong Kong, Sch Data Sci, Shenzhen 518172, Peoples R China

[2] Univ Oxford, Math Inst, Oxford Man Inst Quantitat Finance, Oxford OX2 6ED, England

[3] St Johns Coll, Oxford OX1 3JP, England

[4] Columbia Univ, Dept Ind Engn & Operat Res, New York, NY 10027 USA

来源：

MANAGEMENT SCIENCE | 2023年 / 69卷 / 04期

关键词：

casino gambling; cumulative prospect theory; time inconsistency; randomization; Skorokhod embedding; RANDOMIZED STRATEGIES;

D O I：

10.1287/mnsc.2022.4414

中图分类号：

C93 [管理学];

学科分类号：

12 ; 1201 ; 1202 ; 120202 ;

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.

引用

页码：2474 / 2496

页数：23

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