| Summary: | 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 precommitted 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 precommitted gambler, asymptotically, adopts a loss-exit strategy, a gain-exit strategy, or a nonexit strategy. For a specific parameter setting when the utility function is piecewise power and the probability weighting functions are concave power, we derive the optimal strategy of the precommitted 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 precommitted gambler. In particular, for most empirically relevant cumulative prospect theory parameter values, a precommitted gambler takes a loss-exit strategy while a naive agent does not stop with probability one at any loss level.
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