Multidimensional Measure of Risk: Prospect Rating Vector (PRV)

Single-dimensional measures of risk, such as variance, semi-variance, entropy, etc., are necessarily incomplete. Aggregating potentially rich sources of information into a single, global index has been a long standing practice in most of economics and operations research. Concepts of utility functions, present values, global cost-benefit indexes, etc., are all characterized by a very inefficient utilization of information on which they are based. Risk, for example, is a multiple criteria concept and should be expressed componentwise, as a vector. Higher moments of probability distributions do not represent multiple criteria but only partial descriptions of a single stochastic criterion: anticipated return on investment. We introduce a multidimensional probabilistic measure of risk — Prospect Rating Vector (PRV). This concept is developed in concordance with the principles of stochastic dominance in a distribution-free framework.