The main tools and cocepts of financial and actuarial theory are designed to handle standards, or even small risk. The … sufficient conditions on the utility function ensure the existence of a non degenerate demand for assets with extreme risk. This …

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 study risk measures for random variables modelling financial positions at …

We consider a class of law-invariant convex risk measures which have a.robust representation of the form ρ …. Using variational methods, an explicit formula for the maximizer is given. We exhibit two examples of such risk measures and …

A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future … sub-additive risk measures can model stochastic and/or ambiguous interest rates or defaultable contingent claims. Several … practical examples are presented and in such contexts cash additive risk measures cannot be used. Several dual representations …

In this paper, we show that coherent upper and lower previsions as well as coherent risk measures are only meaningful … extend coherence to all possible situations of initial wealth. Since a coherent risk measure is the negative of a coherent … lower prevision, all results presented in this paper can easily be reformulated in terms of risk measures. Finally, we …

risk capital needed for a portfolio of random activities should be allocated to its components. The well known allocation … model with expected shortfall as corresponding risk value is a prominent member of this class. Our contribution values also …

risk measure can then be viewed as a functional on a space of continuous-time stochastic processes. We extend the notions … of coherent and convex risk measures to the space of bounded cadlag processes that are adapted to a given filtration …. Then, we prove representation results that generalize earlier results for one- and multi-period risk measures, and we …

expected returns and risk, which arethe key determinants of portfolio choice, affect capital flows in often subtle ways. The …