Measures of risk in economics and finance

Risk is an ill-defined notion, both in the economics and finance theory and in real decision cases. There is a multitude of ways to introduce risk in decision frameworks. Moreover, there are a multitude of measures of risk. This apparent inconsistency is explainable: risk is such a vast concept that it seems difficult to picture it completely in a single measurement. Risk can be viewed as mathematical or objective risk in a normative theory. It can also stand for risk perception or even risk assessment in a descriptive theory. Why is this debate about the relevance of normative theories versus descriptive theories so vigorous? Economic theory is traditionally descriptive. This is usually the unique criterion for accepting or ruling out a paradigm or a model. On this ground, we would be tempted to reject expected utility theory. However, and this explain the actual debate, decision theory is a very unique case in economic theory, where we can have two completely different approaches. If we want to predict the behavior of economic agents when they have to make decisions under uncertainty, then we need a descriptive theory. In that case, we have an outside point of view. On the other hand, if we want to apply our findings to actual decision-making, we need a normative theory to help us make the right choices. We are at an other level, within the model that the descriptive theory is trying to describe. In a sense, our descriptive, theoretical model became real, and like Alice in Wonderland, we are plunged into it. We now need reference points to guide us in this new world. A normative theory can provide us with these landmarks. Both theories are useful, each for its own purpose. As long as we clearly distinguish between the two aspects, normative and descriptive, decision analysis and the underlying risk analysis are powerful tools to guide us in the decision-making process on both grounds. Whether a normative or a descriptive approach is adopted, the risk measures obtained will not be the same. Furthermore, decision-makers wish to emphasize certain preferences and include risk in different manners in the decision process: as an objective, as a constraint, or as a trade-off variable. Several dimensions are included in the perception of risk: it seems that we can isolate the two preeminent dimensions: dread, or possibility of loss, and unknown, either quantified (spread) or not (fundamental uncertainty). Another problem is the loss of information that occurs when we start with a whole probability distribution and end up with only two real numbers, risk and return. Unless the probability distribution has a very specific shape, to picture simply all the characteristics of risk derived from the distribution function in a single measure seems like a difficult. This explains the multitude of measures and the numerous confusions about risk. Integrating all these different components of risk in a single measure now seems difficult. There are many issues at stake: should descriptive and normative theories be unified, or clearly distinguished? Is expected utility theory acceptable as a normative theory? In which case, a good risk measure, fully compatible with expected utility theory, is yet to be found. And as far as the descriptive side of a theory of risk is concerned, using only the probability distribution does not seem to suffice to fully describe cognitive style and risk perception (Blaylock and Rees 1984). What alternative or more general framework should be adopted?Economic