Avoiding zero probability events when computing Value at Risk contributions

This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). We recast the traditional Euler contributions from an expectation conditional on an event of zero probability to a ratio involving conditional expectations whose conditioning events have stricktly positive probability. We derive an analytical form of the proposed representation of VaR contributions for various parametric models. Our numerical experiments show that the estimator using this novel representation outperforms the standard Monte Carlo estimator in terms of bias and variance. Moreover, unlike the existing estimators, the proposed estimator is free from hyperparameters

Understanding Operational Risk Capital Approximations: First and Second Orders

We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA). Our emphasis is to focus on the important loss processes with regard to those that contribute most to capital, the so called high consequence, low frequency loss processes. This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice. From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard); Expected Shortfall (ES) and the Spectral Risk Measure. These then form the capital approximations

Sequential Monte Carlo Samplers for capital allocation under copula-dependent risk models

In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component of the portfolio has to be calculated as an expectation conditional to a rare event, which can be challenging to evaluate in practice. We exploit the copula-dependence within the portfolio risks to design a Sequential Monte Carlo Samplers based estimate to the marginal conditional expectations involved in the problem, showing its efficiency through a series of computational examples

Conformal prediction for frequency-severity modeling

We present a nonparametric model-agnostic framework for building prediction intervals of insurance claims, with finite sample statistical guarantees, extending the technique of split conformal prediction to the domain of two-stage frequency-severity modeling. The effectiveness of the framework is showcased with simulated and real datasets. When the underlying severity model is a random forest, we extend the two-stage split conformal prediction procedure, showing how the out-of-bag mechanism can be leveraged to eliminate the need for a calibration set and to enable the production of prediction intervals with adaptive width

A global observational analysis to understand changes in air quality during exceptionally low anthropogenic emission

This global study, which has been coordinated by the World Meteorological Organization Global Atmospheric Watch (WMO/GAW) programme, aims to understand the behaviour of key air pollutant species during the COVID-19 pandemic period of exceptionally low emissions across the globe. We investigated the effects of the differences in both emissions and regional and local meteorology in 2020 compared with the period 2015–2019. By adopting a globally consistent approach, this comprehensive observational analysis focuses on changes in air quality in and around cities across the globe for the following air pollutants PM2.5, PM10, PMC (coarse fraction of PM), NO2, SO2, NOx, CO, O3 and the total gaseous oxidant (OX = NO2 + O3) during the pre-lockdown, partial lockdown, full lockdown and two relaxation periods spanning from January to September 2020. The analysis is based on in situ ground-based air quality observations at over 540 traffic, background and rural stations, from 63 cities and covering 25 countries over seven geographical regions of the world. Anomalies in the air pollutant concentrations (increases or decreases during 2020 periods compared to equivalent 2015–2019 periods) were calculated and the possible effects of meteorological conditions were analysed by computing anomalies from ERA5 reanalyses and local observations for these periods. We observed a positive correlation between the reductions in NO2 and NOx concentrations and peoples’ mobility for most cities. A correlation between PMC and mobility changes was also seen for some Asian and South American cities. A clear signal was not observed for other pollutants, suggesting that sources besides vehicular emissions also substantially contributed to the change in air quality. As a global and regional overview of the changes in ambient concentrations of key air quality species, we observed decreases of up to about 70% in mean NO2 and between 30% and 40% in mean PM2.5 concentrations over 2020 full lockdown compared to the same period in 2015–2019. However, PM2.5 exhibited complex signals, even within the same region, with increases in some Spanish cities, attributed mainly to the long-range transport of African dust and/or biomass burning (corroborated with the analysis of NO2/CO ratio). Some Chinese cities showed similar increases in PM2.5 during the lockdown periods, but in this case, it was likely due to secondary PM formation. Changes in O3 concentrations were highly heterogeneous, with no overall change or small increases (as in the case of Europe), and positive anomalies of 25% and 30% in East Asia and South America, respectively, with Colombia showing the largest positive anomaly of ~70%. The SO2 anomalies were negative for 2020 compared to 2015–2019 (between ~25 to 60%) for all regions. For CO, negative anomalies were observed for all regions with the largest decrease for South America of up to ~40%. The NO2/CO ratio indicated that specific sites (such as those in Spanish cities) were affected by biomass burning plumes, which outweighed the NO2 decrease due to the general reduction in mobility (ratio of ~60%). Analysis of the total oxidant (OX = NO2 + O3) showed that primary NO2 emissions at urban locations were greater than the O3 production, whereas at background sites, OX was mostly driven by the regional contributions rather than local NO2 and O3 concentrations. The present study clearly highlights the importance of meteorology and episodic contributions (e.g., from dust, domestic, agricultural biomass burning and crop fertilizing) when analysing air quality in and around cities even during large emissions reductions. There is still the need to better understand how the chemical responses of secondary pollutants to emission change under complex meteorological conditions, along with climate change and socio-economic drivers may affect future air quality. The implications for regional and global policies are also significant, as our study clearly indicates that PM2.5 concentrations would not likely meet the World Health Organization guidelines in many parts of the world, despite the drastic reductions in mobility. Consequently, revisions of air quality regulation (e.g., the Gothenburg Protocol) with more ambitious targets that are specific to the different regions of the world may well be required.Peer reviewedFinal Published versio

FungalTraits:A user-friendly traits database of fungi and fungus-like stramenopiles

The cryptic lifestyle of most fungi necessitates molecular identification of the guild in environmental studies. Over the past decades, rapid development and affordability of molecular tools have tremendously improved insights of the fungal diversity in all ecosystems and habitats. Yet, in spite of the progress of molecular methods, knowledge about functional properties of the fungal taxa is vague and interpretation of environmental studies in an ecologically meaningful manner remains challenging. In order to facilitate functional assignments and ecological interpretation of environmental studies we introduce a user friendly traits and character database FungalTraits operating at genus and species hypothesis levels. Combining the information from previous efforts such as FUNGuild and Fun(Fun) together with involvement of expert knowledge, we reannotated 10,210 and 151 fungal and Stramenopila genera, respectively. This resulted in a stand-alone spreadsheet dataset covering 17 lifestyle related traits of fungal and Stramenopila genera, designed for rapid functional assignments of environmental studies. In order to assign the trait states to fungal species hypotheses, the scientific community of experts manually categorised and assigned available trait information to 697,413 fungal ITS sequences. On the basis of those sequences we were able to summarise trait and host information into 92,623 fungal species hypotheses at 1% dissimilarity threshold

A global observational analysis to understand changes in air quality during exceptionally low anthropogenic emission conditions

This global study, which has been coordinated by the World Meteorological Organization Global Atmospheric Watch (WMO/GAW) programme, aims to understand the behaviour of key air pollutant species during the COVID-19 pandemic period of exceptionally low emissions across the globe. We investigated the effects of the differences in both emissions and regional and local meteorology in 2020 compared with the period 2015–2019. By adopting a globally consistent approach, this comprehensive observational analysis focuses on changes in air quality in and around cities across the globe for the following air pollutants PM2.5, PM10, PMC (coarse fraction of PM), NO2, SO2, NOx, CO, O3 and the total gaseous oxidant (OX = NO2 + O3) during the pre-lockdown, partial lockdown, full lockdown and two relaxation periods spanning from January to September 2020. The analysis is based on in situ ground-based air quality observations at over 540 traffic, background and rural stations, from 63 cities and covering 25 countries over seven geographical regions of the world. Anomalies in the air pollutant concentrations (increases or decreases during 2020 periods compared to equivalent 2015–2019 periods) were calculated and the possible effects of meteorological conditions were analysed by computing anomalies from ERA5 reanalyses and local observations for these periods. We observed a positive correlation between the reductions in NO2 and NOx concentrations and peoples’ mobility for most cities. A correlation between PMC and mobility changes was also seen for some Asian and South American cities. A clear signal was not observed for other pollutants, suggesting that sources besides vehicular emissions also substantially contributed to the change in air quality. As a global and regional overview of the changes in ambient concentrations of key air quality species, we observed decreases of up to about 70% in mean NO2 and between 30% and 40% in mean PM2.5 concentrations over 2020 full lockdown compared to the same period in 2015–2019. However, PM2.5 exhibited complex signals, even within the same region, with increases in some Spanish cities, attributed mainly to the long-range transport of African dust and/or biomass burning (corroborated with the analysis of NO2/CO ratio). Some Chinese cities showed similar increases in PM2.5 during the lockdown periods, but in this case, it was likely due to secondary PM formation. Changes in O3 concentrations were highly heterogeneous, with no overall change or small increases (as in the case of Europe), and positive anomalies of 25% and 30% in East Asia and South America, respectively, with Colombia showing the largest positive anomaly of ~70%. The SO2 anomalies were negative for 2020 compared to 2015–2019 (between ~25 to 60%) for all regions. For CO, negative anomalies were observed for all regions with the largest decrease for South America of up to ~40%. The NO2/CO ratio indicated that specific sites (such as those in Spanish cities) were affected by biomass burning plumes, which outweighed the NO2 decrease due to the general reduction in mobility (ratio of ~60%). Analysis of the total oxidant (OX = NO2 + O3) showed that primary NO2 emissions at urban locations were greater than the O3 production, whereas at background sites, OX was mostly driven by the regional contributions rather than local NO2 and O3 concentrations. The present study clearly highlights the importance of meteorology and episodic contributions (e.g., from dust, domestic, agricultural biomass burning and crop fertilizing) when analysing air quality in and around cities even during large emissions reductions. There is still the need to better understand how the chemical responses of secondary pollutants to emission change under complex meteorological conditions, along with climate change and socio-economic drivers may affect future air quality. The implications for regional and global policies are also significant, as our study clearly indicates that PM2.5 concentrations would not likely meet the World Health Organization guidelines in many parts of the world, despite the drastic reductions in mobility. Consequently, revisions of air quality regulation (e.g., the Gothenburg Protocol) with more ambitious targets that are specific to the different regions of the world may well be required.World Meteorological Organization Global Atmospheric Watch programme is gratefully acknowledged for initiating and coordinating this study and for supporting this publication. We acknowledge the following projects for supporting the analysis contained in this article: Air Pollution and Human Health for an Indian Megacity project PROMOTE funded by UK NERC and the Indian MOES, Grant reference number NE/P016391/1; Regarding project funding from the European Commission, the sole responsibility of this publication lies with the authors. The European Commission is not responsible for any use that may be made of the information contained therein. This project has received funding from the European Commission’s Horizon 2020 research and innovation program under grant agreement No 874990 (EMERGE project). European Regional Development Fund (project MOBTT42) under the Mobilitas Pluss programme; Estonian Research Council (project PRG714); Estonian Research Infrastructures Roadmap project Estonian Environmental Observatory (KKOBS, project 2014-2020.4.01.20-0281). European network for observing our changing planet project (ERAPLANET, grant agreement no. 689443) under the European Union’s Horizon 2020 research and innovation program, Estonian Ministry of Sciences projects (grant nos. P180021, P180274), and the Estonian Research Infrastructures Roadmap project Estonian Environmental Observatory (3.2.0304.11-0395). Eastern Mediterranean and Middle East—Climate and Atmosphere Research (EMME-CARE) project, which has received funding from the European Union’s Horizon 2020 Research and Innovation Programme (grant agreement no. 856612) and the Government of Cyprus. INAR acknowledges support by the Russian government (grant number 14.W03.31.0002), the Ministry of Science and Higher Education of the Russian Federation (agreement 14.W0331.0006), and the Russian Ministry of Education and Science (14.W03.31.0008). We are grateful to to the following agencies for providing access to data used in our analysis: A.M. Obukhov Institute of Atmospheric Physics Russian Academy of Sciences; Agenzia Regionale per la Protezione dell’Ambiente della Campania (ARPAC); Air Quality and Climate Change, Parks and Environment (MetroVancouver, Government of British Columbia); Air Quality Monitoring & Reporting, Nova Scotia Environment (Government of Nova Scotia); Air Quality Monitoring Network (SIMAT) and Emission Inventory, Mexico City Environment Secretariat (SEDEMA); Airparif (owner & provider of the Paris air pollution data); ARPA Lazio, Italy; ARPA Lombardia, Italy; Association Agr´e´ee de Surveillance de la Qualit´e de l’Air en ˆIle-de- France AIRPARIF / Atmo-France; Bavarian Environment Agency, Germany; Berlin Senatsverwaltung für Umwelt, Verkehr und Klimaschutz, Germany; California Air Resources Board; Central Pollution Control Board (CPCB), India; CETESB: Companhia Ambiental do Estado de S˜ao Paulo, Brazil. China National Environmental Monitoring Centre; Chandigarh Pollution Control Committee (CPCC), India. DCMR Rijnmond Environmental Service, the Netherlands. Department of Labour Inspection, Cyprus; Department of Natural Resources Management and Environmental Protection of Moscow. Environment and Climate Change Canada; Environmental Monitoring and Science Division Alberta Environment and Parks (Government of Alberta); Environmental Protection Authority Victoria (Melbourne, Victoria, Australia); Estonian Environmental Research Centre (EERC); Estonian University of Life Sciences, SMEAR Estonia; European Regional Development Fund (project MOBTT42) under the Mobilitas Pluss programme; Finnish Meteorological Institute; Helsinki Region Environmental Services Authority; Haryana Pollution Control Board (HSPCB), IndiaLondon Air Quality Network (LAQN) and the Automatic Urban and Rural Network (AURN) supported by the Department of Environment, Food and Rural Affairs, UK Government; Madrid Municipality; Met Office Integrated Data Archive System (MIDAS); Meteorological Service of Canada; Minist`ere de l’Environnement et de la Lutte contre les changements climatiques (Gouvernement du Qu´ebec); Ministry of Environment and Energy, Greece; Ministry of the Environment (Chile) and National Weather Service (DMC); Moscow State Budgetary Environmental Institution MOSECOMONITORING. Municipal Department of the Environment SMAC, Brazil; Municipality of Madrid public open data service; National institute of environmental research, Korea; National Meteorology and Hydrology Service (SENAMHI), Peru; New York State Department of Environmental Conservation; NSW Department of Planning, Industry and Environment; Ontario Ministry of the Environment, Conservation and Parks, Canada; Public Health Service of Amsterdam (GGD), the Netherlands. Punjab Pollution Control Board (PPCB), India. R´eseau de surveillance de la qualit´e de l’air (RSQA) (Montr´eal); Rosgydromet. Mosecomonitoring, Institute of Atmospheric Physics, Russia; Russian Foundation for Basic Research (project 20–05–00254) SAFAR-IITM-MoES, India; S˜ao Paulo State Environmental Protection Agency, CETESB; Secretaria de Ambiente, DMQ, Ecuador; Secretaría Distrital de Ambiente, Bogot´a, Colombia. Secretaria Municipal de Meio Ambiente Rio de Janeiro; Mexico City Atmospheric Monitoring System (SIMAT); Mexico City Secretariat of Environment, Secretaría del Medio Ambiente (SEDEMA); SLB-analys, Sweden; SMEAR Estonia station and Estonian University of Life Sciences (EULS); SMEAR stations data and Finnish Center of Excellence; South African Weather Service and Department of Environment, Forestry and Fisheries through SAAQIS; Spanish Ministry for the Ecological Transition and the Demographic Challenge (MITECO); University of Helsinki, Finland; University of Tartu, Tahkuse air monitoring station; Weather Station of the Institute of Astronomy, Geophysics and Atmospheric Science of the University of S˜ao Paulo; West Bengal Pollution Control Board (WBPCB).http://www.elsevier.com/locate/envintam2023Geography, Geoinformatics and Meteorolog