Abstract

We characterize in terms of primitives on risk preferences the stopping and the continuation regions of optimal stopping problems, where an agent without commitment decides when to stop a diffusion. We consider separately the case of a naive agent who is unaware of the possible time inconsistency and the case of a sophisticated agent who is fully aware of a possible time inconsistency in her behavior. Among other things, we apply the general results to fully characterize the extreme cases of never stopping for the naive and never starting for the sophisticate across an extensive range of non-expected risk preference models.

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