Risk analysis and decision theory: An extended summary

We reconcile Kaplan and Garrick's seminal definition of risk with classical subjective expected utility, filling in the relevant gaps and providing a framework that is ready-to-use in applications. We show that Kaplan and Garrick's "frequency" format can be set in one-to-one correspondence with [26]'s utility theory. Kaplan and Garrick's "probability" format corresponds to the framework of [22] in which epistemic uncertainty is captured by a subjective probability over uncertain events. Finally, Kaplan and Garrick's "probability of frequency" format, the most general one, corresponds to the recently proposed framework of [13], which distinguishes aleatory and epistemic uncertainty in a Bayesian perspective. The classic Kaplan and Garrick's risk triplets are then cast in the powerful setting of axiomatic Decision Theory, with its solid behavioral foundations, allowing one to make explicit the often implicit decisions of a Risk Analysis.