Probability Metrics Applied to Problems in Portfolio Theory

In the paper, we consider the application of the theory of probability metrics in several areas in the eld of nance. First, we argue that specially structured probability metrics can be used to quantify stochastic dominance relations. Second, the methods of the theory of probability metrics can be used to arrive at a general axiomatic treatment of dispersion measures and probability metrics can be used to describe continuity of risk measures. Finally, the methods of probability metrics theory are applied to the benchmark-tracking problem significantly extending the problem setting