When to Quit Gambling, if You Must! by Sang Hu, Jan Obłój, Xun Yu Zhou :: SSRN – SSRN Papers

50 Pages

Posted: 16 Feb 2021

See all articles by Sang Hu

The Chinese University of Hong Kong, Shenzhen

University of Oxford – Mathematical Institute; University of Oxford – Oxford-Man Institute of Quantitative Finance; University of Oxford – Saint John’s College

Columbia University – Department of Industrial Engineering and Operations Research (IEOR)

Date Written: February 5, 2021

Abstract

We develop an approach to solve Barberis (2012)’s casino gambling model 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 an independent randomization, and explain why it is a reasonable assumption. The problem is inherently time-inconsistent due to 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, based on which we derive an optimal precommitted rule which is randomized and Markovian. The analytical treatment enables us to make several predictions regarding a gambler’s behavior, including that with randomization they may enter the casino even when allowed to play only once, that whether they will play longer once they are granted more bets depends on whether they are in a gain or at a loss, and that it is prevalent that a naivite never stops loss.

Keywords: casino gambling, cumulative prospect theory, optimal stopping, probability weighting, time inconsistency, randomization, finite time horizon, Skorokhod embedding, potential function


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