["Mathematical Finance, EarlyView. ", "\nABSTRACT\nProspect theory is arguably the most prominent alternative to expected utility theory. We study the investment or gambling behavior of a prospect theory decision maker who is aware of his time‐inconsistency but lacks commitment. For the empirically relevant prospect theory specifications, we obtain the extreme prediction that such a decision maker never gambles or invests in the stock market—even if expected gains are arbitrarily high. Our analysis illustrates some of the challenges in applying prospect theory to dynamic settings."]