Path-Dependent and Randomized Strategies in Barberis' Casino Gambling Model

15 Pages Posted: 8 Dec 2014 Last revised: 16 Jun 2016

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: June 15, 2016

Abstract

We consider the dynamic casino gambling model initially proposed by Barberis [Manage. Sci., 2012, 58, 35-51] and study the optimal stopping strategy of a pre-committing gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis [2012] can be strictly improved by reviewing the betting history or by tossing an independent coin, and we explain that the improvement generated by using randomized strategies results from the lack of quasi-convexity of CPT preferences. Moreover, we show that any path-dependent strategy is equivalent to a randomization of path-independent strategies.

Keywords: casino gambling; cumulative prospect theory; path-dependence; randomized strategies; quasi-convexity; optimal stopping

JEL Classification: D03; D81

Suggested Citation

He, Xue Dong and Hu, Sang and Obloj, Jan K. and Zhou, Xunyu, Path-Dependent and Randomized Strategies in Barberis' Casino Gambling Model (June 15, 2016). Available at SSRN: https://ssrn.com/abstract=2534936 or http://dx.doi.org/10.2139/ssrn.2534936

Xue Dong He

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 (Contact Author)

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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