Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

4.4 Choosing an Adequate Risk Measure – Decision-Theory Aspects

This section will provide a closing discussion on the choice of risk measures, taking into account both decision-theory arguments and practical study goals and experience.

4.4.1 The Salient Goal Involved

Let us recall firstly the variety of goals involved in a risk and uncertainty study for which the risk measure is to be chosen:

• Understand (U) or Accredit (A) are somewhat upstream goals.
• Select (S) or Comply (C) are goals involving full decision-making.

The two former goals may either be part of a larger process targeting eventually one of the two latter goals or may be considered as such within an upstream approach.

When targeting U or A within an upstream approach, a quantity of interest should help in measuring the amount of uncertainty with respect to which it is possible to understand the model and control its accuracy broadly. When nothing else is specified for goal U, variance is a typical choice as an efficient quantity of interest with respect to which one may explore the space of uncertain inputs, that is of risk and uncertainty factors. Probability may be viewed more as a space-filling exploratory tool than a true representation of the decision-maker's belief or preference for the space of possible values and the exploration would rather benefit from randomising as many factors as possible, even those for which the choice of distribution is a difficult task (as discussed in Section 4.2). Goal A may either ...