We consider a dynamic portfolio selection problem in a finite horizon binomial market model, composed of a non-dividend-paying risky stock and a risk-free bond. We assume that the investor’s behavior distinguishes between gains and losses, as in the classical cumulative prospect theory (CPT). This is achieved by considering preferences that are represented by a CPT-like functional, depending on an S-shaped utility function. At the same time, we model investor’s beliefs on gains and losses through two different epsilon-contaminations of the “real-world” probability measure. We formulate the portfolio selection problem in terms of the final wealth and reduce it to an iterative search problem over the set of optimal solutions of a family of non-linear optimization problems.