This paper unifies the work on multiple reinsurers, distortion risk measures, premium budgets,and heterogeneous beliefs …. An insurer minimizes a distortion risk measure, while seekingreinsurance with finitely many reinsurers. The reinsurers … examples withthe Conditional Value-at-Risk illustrate our results …

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 … individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in …

determined by some distortion risk measures with different distortion operators. Under the constraint that a reinsurance policy … is feasible only if the resulting risk of each party is below some pre-determined values, we derive explicit expressions … cases when both parties' risks are measured by Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are studied in great …

This paper presents a random risk measure, named as the random distortionrisk measure. The random distortion risk … measure is a generalization of thetraditional deterministic distortion risk measure by randomizing thedeterministic distortion … function and the risk distribution respectively,where a stochastic distortion is introduced to randomize the distortionfunction …