Optimal Exit Time from Casino Gambling: Strategies of Pre-Committed and Naive Gamblers

26 Pages Posted: 31 Oct 2015 Last revised: 28 Mar 2019

See all articles by Xue Dong He

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

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: March 26, 2019

Abstract

We consider a casino gambling model with an indefinite end date and gamblers endowed with cumulative prospect theory preferences. We study the optimal strategies of a pre-committed gambler, who commits her future selves to the strategy she sets up today, and of a naive gambler, who is unaware of time-inconsistency and may alter her strategy at any time. We identify conditions under which the pre-committed gambler, asymptotically, adopts a loss-exit strategy, a gain-exit strategy, or a non-exit strategy. For a specific parameter setting when the utility function is piece-wise power and the probability weighting functions are concave power, we derive the optimal strategy of the pre-committed gambler in closed form whenever it exists, via solving an infinite dimensional program. Finally, we study the actual behavior of the naive gambler and highlight its marked differences from that of the pre-committed gambler. In particular, for most of empirically relevant CPT parameter values, a pre-committed gambler takes a loss-exit strategy while a naive agent does not stop with probability one at any loss level.

Keywords: casino gambling, cumulative prospect theory, optimal stopping, pre-committed gamblers, naive gamblers, optimal strategies

JEL Classification: C61, D81, G19

Suggested Citation

He, Xue Dong and Hu, Sang and Obloj, Jan K. and Zhou, Xunyu, Optimal Exit Time from Casino Gambling: Strategies of Pre-Committed and Naive Gamblers (March 26, 2019). Available at SSRN: https://ssrn.com/abstract=2684043 or http://dx.doi.org/10.2139/ssrn.2684043

Xue Dong He (Contact Author)

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

Sang Hu

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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