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...

We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.

We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.