Extreme Risks and Rare Events

Recent events and major crisis have revealed the inability of modern societies to anticipate and cope with extreme risks, not only in finance but also in many other fields: epidemiological risk, food security issues, environmental disasters, major industrial accidents. How to model, estimate and regulate such risks has become a major issue in modern societies. First, adequate models of dependence are required, in particular to properly model the occurrence of extreme risks, conditional on current conditions. An immediate next step is to work out the required tools of statistical inference. Finally, developing relevant simulation techniques for rare events is an important and challenging topic.  Researchers at Labex MME-DII are working at the frontier of this research agenda, designing statistical and econometric methods for analyzing and predicting extreme events, as well as applying these methods to financial market data, evaluation of food risk, natural disasters, environmental risk and insurance

Topics in Extreme Risks and Rare Events:

Statistical and econometric methods: Applications:
  • Extremes values theory
  • Ruin theory
  • Weak dependencies
  • Long-range dependence
  • Bootstrap methods
  • Distribution of extreme asset returns
  • Derivative markets
  • Environmental risks
  • Food and health risk
  • Natural disasters

Researchers with interest in Extreme Risk and Rare Events

Patrice Bertail (MODAL’X)

My main current research is concerned with developing extensions of bootstrap, extremes values theory and ruin theory and related estimation procedures in the framework of multidimensional dependent data, including markovian models as well as models satisfying some weak mixing conditions.
Some current works also deal with the use of survey sampling theory when dealing with big data. The idea is to design some appropriate survey sampling plans to practically and efficiently  estimate some characteristics of interest (tails, moments, general empirical measures) when the dataset of interest is too big to be fully usable.

Paul Doukhan (AGM)

Séries temporelles, théorèmes limites sous des conditions de dépendance, dépendance faible, dépendance à longue portée, extrêmes, non stationnarité, applications en économétrie, génétique, écologie.

Nathanaël Enriquez (MODAL’X)

A common point between several recent works of mine can be described as the study of the impact of random environments on usual mathematical objects among which you can find random walks on the line, distances in the plane, spectrum of graphs and matrices. Besides, I am working on stochastic geometry, namely on the properties of the Poisson-Voronoi tesselation of a surface. I am also currently supervising a thesis about probabilistic methods of counting convex lattice polygons.

Ana Karina Fermin (MODAL’X)

Inverse problems: regularization methods and model selection; Iterative and stochastic methods; Seismic tomography; Pharmacokynetic and pharmacodynamic: non lineal mixed effect models; Learning and experimental design: kernel methods (SVM, kriging), experimental design, active learning and model selection; Extreme value theory

Jose-Gregorio Gomez (AGM)

Je travaille sur des questions liées à la théorie des valeurs extrêmes des processus et des champs aléatoires. Spécifiquement sur les théorèmes limites des fonctionnelles de cluster d’extrêmes pour processus faiblement dépendants, inspirée par les résultats sur fonctionnes de queue de distribution par H. Drees et H. Rootzén, par les généralisations de fonctionnelles de cluster d’extrêmes de Johan Segers, et bien sûr, par les résultats sur le mélange et la dépendance faible de Paul Doukhan.

Meglena Jeleva (ECONOMIX)

My research is focused on the impact of uncertainties (probabilistic or not), and their perception, on individual and public short term and long term risk management decisions. Three topics can be identified in my recent theoretical and experimental research and in my projects: (i) optimal environmental policies design under scientific and technological uncertainties, (ii) insurance decisions concerning standard and extreme risks (iii) intertemporal preferences representation allowing ambiguity attitudes to change over time, and in relation with the decision maker’s past experience.

Ahmed Kebaier (LAGA)

I am interested in several topics related to financial applications. I study the improvement of the well know Multilevel Monte Carlo method in order to decrease the bias in the approximation of options prices. I am also studying the use of the Multilevel Monte Carlo methods for the computation of the probability of company defaults, extreme risks and rare events. I am also interested in estimating the parameters of financial models when their paths are observed such as the popular Cox-Ingersoll-Process (with and without jumps), and the well-known Wishart processes.

Marie Kratz (CERESSEC)

Extreme value theory; Quantitative risk management; Gaussian random fields; Excursion sets

François Longin (CERESSEC)

François Longin pursues a career in banking and finance by allying research, consulting and training. His thesis was about extreme movements in financial markets such as stock market crashes. For many years he has been working on the applications of extreme value theory to financial markets: the statistical distribution of extreme returns, the setting of margins in derivatives markets, the impact of financial regulation on market volatility, the improvement of portfolio management techniques during highly volatile periods, the computation of value at risk for market positions, the definition of catastrophe scenarios for stress testing… His research has been applied by financial institutions in the risk management area. François is currently a financial consultant and his domain of expertise covers risk management for financial institutions, financial management for non-financial firms and wealth management for individuals. He also participates in the SimTrade project (pedagogical tool in financial market).

Philippe Soulier (MODAL’X)

Mon domaine de recherche est l’étude probabiliste et statistique de processus stochastiques à mémoire longue, à distribution marginale à variation régulière et dont la dynamique est non linéaire, et des applications de ces processus à la modélisation dans des domaines variés dont les séries financières et le télétraffic.

Charles Tillier (MODAL’X)

Food safety is now receiving increasing attention, both in the public health community and in the scientific literature. In the beginning, static approaches were developed, in which the exposure to a contaminant is calculated based on consumption data and contamination (or analytical) data. Recent works focus on static approaches for modeling the quantity of a specific food contaminant ingested over a short period of time. One difficulty for studying food contamination is the dimensionality
of the problem since a given contaminant may occur in a very large number of products. Besides, heavy tail phenomena and temporal dependence are at the core of food and climatic risks analysis. Intuitively, heavy tail phenomena are those where the extremes values are important compared with other values (hurricane, large food contaminant doses, like methylmercury, ochratoxin…). The traditional risk analysis under the assumption that the observations (consumption, contaminants or environmental risk factors) are independent, leads to a systematic underestimation of risks. Mathematical models taking into account the interplay between temporal and spatial dependencies (consumptions dynamic, pharmakocinetic elimination phenomenon, correlations between contaminants and different factors) will allow to better characterize populations at risk. Quantifying the link between the dependence and the heavy tails is a major issue for applications and prudential decisions.