On risk measures and decisions in insurance and finance

In this paper, we argue that a distinction exists between risk measures and
decision principles. Though both are functionals assigning a real number to a random
variable, we think there is a hierarchy between the two concepts. Risk measures
operate on the first "level", quantifying the risk in the situation under consideration,
while decision principles operate on the second "level", often being derived from
the risk measure. We illustrate this distinction with several canonical examples of
economic situations encountered in insurance and finance.
Special attention is paid to the role of axiomatic characterizations in determining
risk measures and decision principles. Some new axiomatic characterizations of
families of risk measures and decision principles are also presented.
Keywords: Risk measurement; Decision-making; Axiomatization; Measure of risk;
Premium principles; Solvency capital principles; Risk transfer principles; Equivalent
utility; Esscher transform; Exponential utility.
JEL-Classification: D81; G10; G20.
MSC-Classification: 62P05.