Natural catastrophes attract regularly the attention of media and have become a source of public concern. From a financial viewpoint, natural catastrophes represent idiosyncratic risks,diversifiable at the world level. But for reasons analyzed in this pap er reinsurance markets are unable to...

In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for time-consistent convex monetary risk measures in terms of one-step penalty functions. We first...

We consider a class of law-invariant convex risk measures which have a.robust representation of the form ρ(X ) = ...... . The supremum is taken over the set of all Radon Nikodym derivatives corresponding to the set of all probability measures on B(0,1] which are absolutely continuous with...