= -E[X; X < 0]
Words are flexible, and their meaning need not be fixed. Scientists can adapt the meanings of words to their needs, as long as everybody understands what they are talking about, in their branch of research. The problem with the use of the word ‘risk’ in statistics and economics is that its concept is very basic. The word is also used in common language and for the communication with decision makers and the general public. It appears that there is some confusion, so that the flexibility of words leads to conceptual errors. By defining and fixing the concepts involved as suggested in the two papers below, and by sticking to the meaning in the natural language, much clarity is gained. It turns out that textbooks generally can keep their mathematics but will best rewrite their texts to these definitions. Not only the students and the general public will benefit from this sudden clarity, but eventually also statistics and economic theory themselves.
(2) Measuring Utility (Chapter
8 of "Voting Theory for Democracy") (PDF 1.5 MB)
(Inclusion of above risk measure in utility gives a better representation.)
(3) Risk in the lognormal distribution (New section in "The Economics Pack") (PDF 0.4 MB)
Note: this page takes precedence on my earlier working papers on risk,
referred to elsewhere in this site.