  We propose a novel class of convex risk measures, based on the concept of the
Fr\'echet mean, designed in order to handle uncertainty which arises from
multiple information sources regarding the risk factors of interest. The
proposed risk measures robustly characterize the exposure of the firm, by
filtering out appropriately the partial information available in individual
sources into an aggregate model for the risk factors of interest. Importantly,
the proposed risks can be expressed in closed analytic forms allowing for
interesting qualitative interpretations as well as comparative statics and thus
facilitate their use in the everyday risk management process of the insurance
firms. The potential use of the proposed risk measures in insurance is
illustrated by two concrete applications, capital risk allocation and premia
calculation under uncertainty.
