When to Quit Gambling, if You Must!

50 Pages Posted: 16 Feb 2021

See all articles by Sang Hu

Sang Hu

The Chinese University of Hong Kong, Shenzhen

Jan Obłój

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

Xun Yu Zhou

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

Suggested Citation

Hu, Sang and Obloj, Jan K. and Zhou, Xunyu, When to Quit Gambling, if You Must! (February 5, 2021). Available at SSRN: https://ssrn.com/abstract=3779900 or http://dx.doi.org/10.2139/ssrn.3779900

Sang Hu (Contact Author)

The Chinese University of Hong Kong, Shenzhen ( email )

Shenzhen
China

Jan K. Obloj

University of Oxford - Mathematical Institute ( email )

AWB, ROQ, Woodstock Rd
Oxford, OX2 6GG
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

University of Oxford - Saint John's College ( email )

St Giles
Oxford, Oxon OX1 3JP
United Kingdom

Xunyu Zhou

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

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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