ORDERINGS AND RISK PROBABILITY FUNCTIONALSIN PORTFOLIO THEORY

摘要

This paper studies and describes stochastic orderings ofrisk/reward positions in order to define in a natural way risk/reward mea-sures consistent/isotonic to investors' preferences. We begin by discussingthe connection between the theory of probability metrics, risk measures,distributional moments, and stochastic orderings. Then we examine severalclasses of orderings which are generated by risk probability functionals. Fi-nally, we demonstrate how further orderings could better specify the in-vestor's attitude toward risk.