Subjective risk measures: Bayesian predictive scenarios analysis

In this paper we study methods for measuring risk. First, we introduce a conditional risk measure and point out that it is a coherent risk measure. Using the Bayesian statistical idea a subjective risk measure is defined. In some special cases, closed form expressions for the risk measures can be obtained. The credibility theory can be used to relax the strong assumptions on the model and prior distributions, and to obtain approximated risk measure formulas. Applications in both finance and insurance are discussed.