Most economic models are prescriptive and based on expected utility theory. Decisions taken on the basis of these models ought to be completely rational and consistent with axioms of the expected utility theory. Prospect theory (PT) is an alternative theory of choice under risk and increasingly used to explain deviations from the traditional paradigm of rational agents. It is important to understand the concept of the PT and its cumulative representation, as well as how it is measured and whether and to what extent PT supports real decisions under risk. This article explores these questions and deliver some axiomatic research review of Cumulative Prospect Theory (CPT) as a framework for decision under risk.