  We study the problem of selling an asset near its ultimate maximum in the
minimax setting. The regret-based notion of a perfect stopping time is
introduced. A perfect stopping time is uniquely characterized by its optimality
properties and has the following form: one should sell the asset if its price
deviates from the running maximum by a certain time-dependent quantity. The
related selling rule improves any earlier one and cannot be improved by further
delay. The results, which are applicable to a quite general price model, are
illustrated by several examples.
