Optimal Stopping in a Dynamic Salience Model

Models of non-linear probability weighting, such as cumulative prospect theory, predict time-inconsistent behavior when applied to a dynamic context (e.g., Machina, 1989). While time-inconsistent behavior is indeed widespread, common specifications of CPT have (too) extreme implications in certain setups (e.g., Ebert and Strack, 2015, 2018). In this study, we compare the implications of (exogeneous) probability weighting as assumed in CPT to those of (endogenous) probability weighting as proposed in salience theory of choice under risk (Bordalo et al., 2012), under the (testable) assumption that the decision maker is naive about his time-inconsistency.

We propose a dynamic salience model to study the choice of when to optimally stop an arithmetic brownian motion with non-positive drift. Our salience model predicts that the optimal stopping behavior is sensitive to the drift of the process; namely, a naive agent will gamble if the drift of the process is slightly negative, but will stop immediately if the drift becomes too negative. This prediction is arguably more plausible than those of CPT, which under common specifications predicts excessive gambling irrespective of the drift of the process, and EUT (with a concave utility function), which predicts no gambling at all.