We propose a novel class of convex risk measures, based on the concept of the Fréchet 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.

Clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space. Such type of clustering approaches are highly appreciated in many fields where the observational/experimental error is significant or the data nature is more complex and the traditional learning algorithms are not applicable or effective to treat. Under this perspective, each observation is identified by an appropriate probability measure and the proposed clustering schemes rely on discrimination criteria that utilize the geometric structure of the space of probability measures through core techniques from the optimal transport theory. The advantages and capabilities of the proposed approach and the geodesic criterion performance are illustrated through a simulation study and the implementation in two different applications: (a) clustering eurozone countries’ bond yield curves and (b) classifying satellite images to certain land uses categories.

This study presents a novel approach to assessing food security risks at the national level, employing a probabilistic scenario-based framework that integrates both Shared Socio-economic Pathways and Representative Concentration Pathways. This innovative method allows each scenario, encompassing socio-economic, and climate factors, to be treated as a model capable of generating diverse trajectories. This approach offers a more dynamic understanding of food security risks under varying future conditions. The paper details the methodologies employed, showcasing their applicability through a focused analysis of food security challenges in Egypt and Ethiopia, and underscores the importance of considering a spectrum of socio-economic and climatic factors in national food security assessments.