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