Subjective risk measures: Bayesian predictive scenarios analysis

In this paper we study methods for measuring risk. First, we introduce a co nditional risk measure and point out that it is a coherent risk measure. Us ing the Bayesian statistical idea a subjective risk measure is defined. In some special cases, closed form expressions for the risk measures can be ob tained. The credibility theory can be used to relax the strong assumptions on the model and prior distributions, and to obtain approximated risk measu re formulas. Applications in both finance and insurance are discussed. (C)1 999 Elsevier Science B.V. All rights reserved.