In trading stocks investors naturally aspire to "buy low and sell high (BLSH)". This paper formalizes the notion of BLSH by formulating stock buying/selling in terms of four optimal stopping problems involving the global maximum and minimum of the stock prices over a given investment horizon....

We formulate an optimal stopping problem where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses...