Final Report Summary - RARE (Risk Analysis, Ruin and Extremes) The RARE acronym stands for Risk Analysis, Ruin and Extremes. The project is focusing on developing the theoretical side of the analysis of risk, in case of disasters or extreme shocks, for financial or environmental risk pools. The main goal of this project is the stochastic analysis of complex risk models and their extremes. In focus are both continuous and discrete time multidimensional vector-valued processes that suitably approximate and model insurance risk, queues, financial portfolios, just to mention a few. From the methodological point of view this project envisages various extensions of classical tools and approaches in extreme value theory, asymptotic theory including the double-sum method, comparison method of Gaussian measures, Slepian’s inequality, Mitra-Resnick methodology. In addition to developing new risk measures, the evaluation of the effect of aggregated risks is another central topic in the prediction of financial or natural disasters, with direct connotations into risk management. Since specialists working on the areas of extremes and rare events are scarce and sparse, such an exchange program helps creating a needed network of knowledge, ideas and experience. The initial RARE network has been formed of 20 experienced researchers and 20 early stage researchers from 12 international leading research centers from several European and non-European, emerging and developed countries: Australia, China, France, India, Japan, Poland, Russia, Switzerland, UK and USA. At the end of the four years, the group united over a hundred researchers from the initial network institutions and other world leading research centers. More and more researchers adhered to the RARE network, participating in its events and being involved in RARE publications, including its special issues. Thus, at the end of the four years, the group united over a hundred researchers from the initial network institutions and other world leading research centers. New research teams in several partner institutions have by now significantly increased and fully established themselves in the field. For instance the Institute for Financial and Actuarial Mathematics of the University of Liverpool increased from 4 members at the beginning of the project to 12 by the end of it. Another example is the foundation by one of the scientific coordinators of a new research center within ESSEC Business School (in Paris and Singapore) dedicated to quantitative risk analysis and management, CREAR, which in 2017 turned 4 years old. Description of the work performed:The scientific output of the project is overwhelming, with over 200 scientific articles published and submitted for publication, outlining results ranging from new concepts on rare events analysis, new risk measures, extreme behavior analysis to improvements on existing risk analysis tools and statistical applications. The merit of the project is that several important ideas have materialized thanks to intense networking and collaborations of different experts. The first two years were used for “getting to know each other” research interests and expertise, by meeting the full teams from partners institutions, while setting out initial mini-projects along the two directions of research proposed, “new developments on extreme rare events” and “risk modeling.“ The last two years of the project were dedicated to raising awareness regarding rare and extreme events and significantly increased the visibility of the key researchers in the field. The excellence of the RARE conferences, workshops, seminars, special lectures, industry seminars, publications and its special issue contributed to the success of the network and its ethos. Among the highlights of RARE activities is the kick-off workshop held at ISI Kolkata, were a large number of EU partners participated alongside non-EU partners and other well-renowned professors in Extreme Value Theory from all over the world. The entire community has welcomed then the RARE initiative. The RARE workshop held at Nankai University during the second year of the project managed to gather all the RARE partners in one place and thus to set-up directions of research and research exchanges. The third year featured the organization of two well-known international conferences in Liverpool, coordinator of RARE, one for young researchers, PARTY, acronym for Perspectives on Actuarial Risks in Talks by Young researchers, and a second one, the largest annual international congress in Insurance: Mathematics and Economics, IME2015. The highest point of RARE activities was reached by its Concluding workshop held in La Baule, France, during the last year of the project. More than 60 world experts gathered in this charming resort city. It featured a special lecture on Bonus-Malus systems for car insurance held by Prof Lemaire (Wharton, USA), serendipitous given that La Baule is the "brithplace of Bonus-Malus". The final round table of the event, gathered leading researchers from both academia and practice, discussing "The Way Forward". The discussants talked about interconnections, multi-disciplinarity, transformation of uncertainty into measurable risks, "ultimate risk", business decisions, impact of decisions, global effects, global modelling, artificial intelligence, role of regulators, communication and new democratic systems, in front of an attentive audience of experts coming from the 5 continents. It is a testimony to the broad reach of the RARE community and the scope of its work. A special edition of the Annals of Actuarial Science will contain selected papers presented at the workshop and will no doubt constitute a reference issue in the field.Scientific output and impact of RARE:The project aims at understanding the financial risks involved in various financial activities (insurance, banking), with impact on risk management and the environmental risks, with effects on the climate change research. Based on the contacts with industry of some of the partners, RARE is able to provides assistance on concrete practical issues, as, for instance, the Solvency tests from insurance industry, by improving existing toolkits for risk modeling, quantification and assessment of risks, evaluation and management of any fields faced with random events, competitive markets and thus risk management. The scientific output of the project spans results ranging from applied probability, statistics, to queuing theory, game theory, approximation theory, financial mathematics, risk management and insurance. Interesting findings concern the new concept of Parisian ruin, models for complex dependence structures, comparison methodology for Gaussian arrays and related processes, new risk measures, approximation of Gaussian chaos, new martingale identification methods, fractional calculus, fraction and G-Brownian motion, Piterbarg property of certain Gaussian fluid queues, extreme behavior of general non-homogeneous Gaussian fields, approximation of processes with variable smoothness, Normex, bonus-mauls systems, the winner’s curse, just to mention a few. The RARE publications, workshops, seminars, its special sessions at international events, special issues in applied probability journals, partners and affiliated members are journalized on the project website https://www.liv.ac.uk/institute-for-financial-and-actuarial-mathematics/rare/. The published results are well cited and paved the way for successful research within RARE and beyond. Further to that, most of RARE publications are posted on the mathematical arXiv.org website, accessible to researchers worldwide.In addition to the scientific impact on the applied probability literature and the financial industry, the most impacted by the RARE exchange scheme were the early career researchers involved in the project, which ranged from PhD students to post-doctoral fellows and further early career academics. They all benefited from being fast connected to a network of world-class researchers, inspired and mentored during the regular networking activities and nonetheless exposed to high educational trainings during the short-courses, schools or RARE workshops. Moreover, as members of the RARE network, all partner institutions attracted more early career researchers, by providing them with the exposure to a mixture of research structures: math departments, business schools, financial laboratories and institutes. The RARE research and training program seems to be only the beginning of long-term cooperation between partners, since their complementary roles proved to be mutually beneficial. Joint educational-research programs have being discussed and already implemented among RARE partners, other grant applications thought-out and exchanges between European and Non-European institutions perpetuate grace to the Marie-Curie IRSES scheme.
