Technical Note—Path-Dependent and Randomized Strategies in Barberis’ Casino Gambling Model

Xue Dong He (), Sang Hu (), Jan Obłój () and Xun Yu Zhou ()
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Xue Dong He: Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong
Sang Hu: School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China
Jan Obłój: Mathematical Institute, Oxford-Man Institute of Quantitative Finance and St John’s College, University of Oxford, Oxford OX2 6GG, United Kingdom
Xun Yu Zhou: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027

Operations Research, 2017, vol. 65, issue 1, 97-103

Abstract: We consider the dynamic casino gambling model initially proposed by Barberis (2012) and study the optimal stopping strategy of a precommitting gambler with cumulative prospect theory (CPT) preferences. We illustrate how the strategies computed in Barberis (2012) [Barberis N (2012) A model of casino gambling. Management Sci. 58(1): 35–51.] 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 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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