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

Abstract

We employ the casino gambling model in He et al (2015) (available at: http://ssrn.com/abstract=2534936) to study the strategies of a pre-committed gambler, who commits her future selves to the strategy she sets up today, and of a naive gambler, who fails to do so and thus keeps changing plans at every time. We identify conditions under which the pre-committed gambler, asymptotically, adopts a stop-loss strategy, exhibits the behavior of disposition effect, or does not exit. 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. Finally, we study the actual behavior of the naive gambler and highlight its marked differences from that of the pre-committed gambler.The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2682637