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

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