Until the Bitter End: on Prospect Theory in the Dynamic Context

We show that already a small amount of probability weighting has strong implications for the application of prospect theory in the dynamic context. A naive agent will never stop a stochastic process that represents his wealth. This holds for a very large class of processes, and independently of the reference point and the curvatures of the value and weighting functions. This dynamic result is a consequence of a static result that we call skewness preference in the small: At any wealth level there exists an arbitrarily small gamble (which is sufficiently rightskewed) that a prospect theory agent wants to take. By choosing a proper stopping strategy the agent can always implement such a gamble and thus never stops. We illustrate the implications for dynamic decision problems such as irreversible investment, casino gambling, and the disposition effect.