Robust Optimal Risk Sharing and Risk Premia in Expanding Pools

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectively or subjectively given probabilistic model. Next, we develop a robust approach by explicitly taking uncertainty about the probabilistic model (ambiguity) into account. The resulting robust certainty equivalents and risk premia compound risk and ambiguity aversion. We provide explicit results on their limits and rates of convergence, induced by Pareto optimal risk sharing in expanding pools

Modeling and pricing cyber insurance: Idiosyncratic, systematic, and systemic risks

The paper provides a comprehensive overview of modeling and pricing cyber insurance and includes clear and easily understandable explanations of the underlying mathematical concepts. We distinguish three main types of cyber risks: idiosyncratic, systematic, and systemic cyber risks. While for idiosyncratic and systematic cyber risks, classical actuarial and financial mathematics appear to be well-suited, systemic cyber risks require more sophisticated approaches that capture both network and strategic interactions. In the context of pricing cyber insurance policies, issues of interdependence arise for both systematic and systemic cyber risks; classical actuarial valuation needs to be extended to include more complex methods, such as concepts of risk-neutral valuation and (set-valued) monetary risk measures

Unconventional charge-density-wave gap in monolayer NbS2_2

Using scanning tunneling microscopy and spectroscopy, for a monolayer of transition metal dichalcogenide H-NbS$_2$ grown by molecular beam epitaxy on graphene, we provide unambiguous evidence for a charge density wave (CDW) with a 3$\times$3 superstructure, which is not present in bulk NbS$_2$. Local spectroscopy displays a pronounced gap of the order of 20 meV at the Fermi level. Within the gap low energy features are present. The gap structure with its low energy features is at variance with the expectation for a gap opening in the electronic band structure due to a CDW. Instead, comparison with \it{ab initio} calculations indicates that the observed gap structure must be attributed to combined electron-phonon quasiparticles. The phonons in question are the elusive amplitude and phase collective modes of the CDW transition. Our findings advance the understanding of CDW mechanisms in two dimensional materials and their spectroscopic signatures

The Cryptic African Wolf: Canis aureus lupaster Is Not a Golden Jackal and Is Not Endemic to Egypt

The Egyptian jackal (Canis aureus lupaster) has hitherto been considered a large, rare subspecies of the golden jackal (C. aureus). It has maintained its taxonomical status to date, despite studies demonstrating morphological similarities to the grey wolf (C. lupus). We have analyzed 2055 bp of mitochondrial DNA from C. a. lupaster and investigated the similarity to C. aureus and C. lupus. Through phylogenetic comparison with all wild wolf-like canids (based on 726 bp of the Cytochrome b gene) we conclusively (100% bootstrap support) place the Egyptian jackal within the grey wolf species complex, together with the Holarctic wolf, the Indian wolf and the Himalayan wolf. Like the two latter taxa, C. a. lupaster seems to represent an ancient wolf lineage which most likely colonized Africa prior to the northern hemisphere radiation. We thus refer to C. a. lupaster as the African wolf. Furthermore, we have detected C. a. lupaster individuals at two localities in the Ethiopian highlands, extending the distribution by at least 2,500 km southeast. The only grey wolf species to inhabit the African continent is a cryptic species for which the conservation status urgently needs assessment

Statement on a conceptual framework for the risk assessment of certain food additives re-evaluated under Commission Regulation (EU) No 257/2010

The Panel on Food Additives and Nutrient Sources added to Food (ANS) provides a scientific statement presenting a conceptual framework for the risk assessment of certain food additives re-evaluated under Commission Regulation (EU) No 257/2010. This framework will be used in the evaluation made by the Panel, but the expert judgement of the scientific background, on a case-by-case basis, remains essential to reach a final conclusion. The outcome of the re-evaluation of food additives taking into account all available information is presented in the document, as well as the exposure assessment scenarios to be carried out by the Panel considering the use levels set in the legislation and the availability of adequate usage or analytical data

Convex Capital Requirements for Large Portfolios

For a large homogeneous portfolio of financial positions, we study the asymptotic behavior of the capital requirement per position defined in terms of a convex monetary risk measure. In an actuarial context, this capital requirement can be seen as a premium per contract. We show that the premia converge to the fair premium as the portfolio becomes large, and we give a precise description of the decay of the risk premia. The analysis is carried out first for a law-invariant convex risk measure and then in a situation of model ambiguity

Potentials of a Markov process are expected suprema

Expected suprema of a function f observed along the paths of a nice Markov process define an excessive function, and in fact a potential if f vanishes at the boundary. Conversely, we show under mild regularity conditions that any potential admits a representation in terms of expected suprema. Moreover, we identify the maximal and the minimal representing function in terms of probabilistic potential theory. Our results are motivated by the work of El Karoui and Meziou (2006) on the max-plus decomposition of supermartingales, and they provide a singular analogue to the non-linear Riesz representation in El Karoui and Föllmer (2005)