Relative deviation metrics and the problem of strategy replication

In the paper, we generalize the classic benchmark tracking problem by introducing the class of relative deviation metrics (r.d. metrics). We consider specific families of r.d. metrics and how they interact with one another. Our approach towards their classification is inspired by the theory of probability metrics — we distinguish between compound, primary and simple r.d. metrics, introduce minimal r.d. metrics, and explore dual forms consistent with a preference order relation defined by a class of utility functions. Finally we focus on r.d. semi-metrics, implied pre-orders and how they can be applied to the problem of beating a benchmark.