On Risk Measures and Decisions in Insurance and Finance∗

In this paper, we argue that there exists a distinction between risk measures and decision principles. Though both can be regarded as functionals assigning a real number to a random variable, we think that 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”, being derived from the risk measure. We will briefly illustrate this distinction with several examples of economic situations encountered in the insurance and financial industry. 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.