Workshop on
Can Stochastic Geometry handle Dynamics of Risk Management?
Lund, April 18-20, 2018
This workshop aims to bring together researchers from academia and risk management research oriented representatives of industry, for a scientific discussion on building bridges between Stochastic Geometry and Risk Management. The emphasis is on description and understanding of dynamics in the risk management.
The represented research fields on the academic side are: dynamical modeling in space and time, excursions sets and stochastic geometry, and risk analysis.
For people from industry, it is important to know which kind of techniques/tools are developed within these research areas. Presenting or discussion an application in any empirical field (as for instance on sea modelling) will stimulate discussion and may promote applications within risk management area. An open ended format of the meeting will be also useful for the involved academics, since they do not use necessarily the same approaches or represent the same views.
However, the central part of the meeting are presentations by professionals from industry and the discussion will evolve around practical problems introduced through those.
Organizing Committee:
Krzysztof Nowicki, Department of Statistics, Lund University, Sweden, Krzysztof.Nowicki@stat.lu.se
Krzysztof Podgórski, Department of Statistics, Lund University, Sweden, Krzysztof.Podgorski@stat.lu.se
Gunilla Roos, Department of Statistics, Lund University, Sweden, Gunilla.Roos@stat.lu.se
Scientific Committee:
Prof. Marie Kratz, ESSEC Business School, CREAR, Paris, France and Department of Statistics, Lund University, Sweden, kratz@essec.edu
Dr. Sreekar Vadlamani, TIFR–Center for Applicable Mathematics, Bangalore, India and Department of Statistics, Lund University, Sweden, Sreekar.Vadlamani@stat.lu.se
Participant
Affiliation
Contribution
Registration/Status
A conditional approach for spatiotemporal risk assessment of random field threshold exceedances
Functionals related to topological and geometrical characteristics of random field excursion sets defined by threshold exceedances are useful, as reference structural indicators, for the description of system dynamics and for risk assessment in a variety of fields of application (e.g. Environment, Health, Geophysics, Engineering, etc.). Risk measures on such indicators, evaluated at varying subregional scales, provide the informational basis for construction of dynamic risk mapping. In many cases, model-based conditional simulation can be used for the empirical characterization of the probability distributions of selected indicators on the basis of available observations. In this talk, we discuss various analytical and methodological aspects regarding the formalization, interpretation and implementation of risk measures under this approach. In particular, we focus on quantile-based risk measures, with emphasis on implications derived from the underlying random field structural complexity. Further, we address issues concerning, specifically, the effect of certain space and state transformations, such as spatial deformation, change of measure related to population exposure, as well as the natural consideration of non-constant thresholds in some scenarios. (Joint work with Ana E. Madrid and José L. Romero-Béjar.)
Confirmed
Calculating excursion sets for latent Gaussian models using the R package excursions
In several areas of application ranging from brain imaging to astrophysics and geostatistics, an important statistical problem is to find regions where the process studied exceeds a certain level. Estimating such regions so that the probability for exceeding the level in the entire set is equal to some predefined value is a difficult problem connected to the problem of multiple significance testing. In this talk, I will describe a method for how this problem can be solved for latent Gaussian models, and introduce the R package excursions that implements the proposed method.
As an illustration of how the package can be used, I will consider an application where precipitation data is modelled as gamma distributed observations with a spatially varying mean value. The mean is in turn modelled by a Gaussian random field, which we want to calculate excursion sets for conditionally on the observed rainfall.
Confirmed
Procyclicality of Empirical Measurements of Risk in Financial Markets
There is an accepted idea that risk measurements are pro-cyclical: in times of crisis, they overestimate the future risk, while they underestimate it in quiet times. We develop a method to quantify this effect and test it on 11 stock indices using the historically estimated VaR on a rolling sample. Using a simple GARCH(1,1) model, we conclude that this pro-cyclical effect is related to the clustering of volatility. At the same time, we show that even iid innovations present pro-cyclicality. It is a deficiency of an approach based on historical estimation of a risk measure defined w.r.t a probability distribution. Instead, we propose to use a stochastic process, as e.g. the sample quantile process, to determine dynamically the future risk.
Confirmed
Dr. Michel Dacorogna, the International Research Chair from LabEx MME-DII & ESSEC CREAR (April-June, 2018)
Modelling Risks Stochastically, Methods and Problems
Since the advent of risk based solvency, insurance companies are required to quantitatively estimate the capital they need to exercise their business. For doing so, many companies have developed stochastic models of the evolution of their business. We present here the basic components of those models and discuss the various assumptions that are need to build them. We show how risk are aggregated to obtain a distribution for the entire portfolio and discuss the various usages of internal models.
Along the way, we present areas of unsolved problems that could be the subject of further research. Moreover, we show new possible developments that would go beyond what people are doing today in terms of risk modelling. Particularly, we discuss the issue of multi-step evolution of the risks and the problems this poses. Such advances would be fundamental to improve the economic valuation of longterm liabilities, which is a condition to design innovative solutions for pension funds.
Confirmed
Level crossings and Applications
We will illustrate the theory of level crossings of stationary Gaussian processes with some applications in optics, oceanography, and medicine
Confirmed
Crest/trough and front/back asymmetric waves in wave energy systems
In a wave energy converting system the wave energy is transformed into electrical energy via a floating energy absorber. In the design stage the movements of the absorber is often simulated using a Gaussian stochastic wave simulated from the power spectrum. The talk will discuss how possible deviations from the Gaussian model, like crest/trough and wave front/back asymmetry, can affect the result of the simulations.
Confirmed
Methods of stochastic geometry for random sets
In many situations, random sets emerge as a 'natural' model for an issue, because they describe the possible values of some functions (or variables) and also the range of values which satisfy certain properties or restrictions (e.g. an excursion set of a threshold). Stochastic geometry provides the theoretical basis as well as the tools to deal with random sets in applications. This also yields statistical methods to analyze corresponding data. In the presentation the capacity functional, which uniquely describes the distribution (i.e. the law) of a random set, will be explained. Since in applications the capacity functional cannot completely be determined, several contact distribution functions are considered which can supply essential partial information for a random set. This will be illustrated for excursion sets (joint work with Marie Kratz).
Confirmed
NA
Organizer
Spatial wave size for Gaussian random fields
A method of measuring three-dimensional spatial wave size is proposed and statistical distributions of the size characteristics are derived in explicit integral forms for Gaussian sea surfaces. New definitions of wave characteristics such as the crest-height, the length, the size and the wave front location are provided in fully dimensional context. The joint statistical distributions of these wave characteristics are derived using the Rices formulas for expected numbers of local maximum and distance from a local maximum to a level crossing countour. Review of the Rice’s method to study crossing distributions is given. The work is jointly and led by Igor Rychlik.
Confirmed
Regularizing asymptotic approach for structural characteristics of random field excursion sets;
Spatial and spatiotemporal risk assessment is an area with an increasing research interest in different disciplines, such as Hydrology, Environmental Sciences, Actuarial Sciences, etc. There are more and more approaches or methodologies that address this issue under suitable regularity assumptions on the underlying random field model representing the phenomenon under analysis. An asymptotic approach based on the well-known Mollifier regularizing sequence is proposed. This allows working with random fields under the hypothesis of sample paths continuity, even Lp sample paths. Relationships between the excursion sets of the reference random field and the transformed sequence, as well as the asymptotic behavior of first-order indicators related to structural properties of excursion sets, useful for risk assessment, are addressed. Finally, since it is usual being interested in a specific level of resolution, the previous relationships are also of relevance for practice. (Joint work with José M. Angulo.)
Confirmed
Colloidal particle aggregation in three dimensions;
Colloidal systems are of importance not only for everyday products, but also for the development of new advanced materials. In all applications, it is crucial to understand and control colloidal interaction. Here, we study colloidal particle aggregation in three dimensions and compare real aggregates of silica nanoparticles to structures obtained by two different models for particle aggregation, the diffusion limited cluster aggregation model and the reaction limited cluster aggregation model, which are both characterized by the probability of particles to aggregate upon collision. We present some methods and models from spatial point process theory and show how these can be applied to estimate the probability of aggregation. First, experimentally obtained and simulated three dimensional structures are compared by means of some summary functions in order to find the most suitable probability. Second, Gibbs point process models are fitted to the data and used to estimate the probability. The data are given in a three-dimensional micrograph obtained by high-angle annular dark field scanning transmission electron microscopy tomography. Joint work with Henrike Häbel, Mats Rudemo, Charlotte Hamngren Blomqvist, Eva Olsson, and Matias Nordin
Confirmed
Classification, calibration, and quantification: A study of dataset shift
Classification is one of the most important statistical techniques, with applications in virtually all quantitative fields including finance and economics. Credit scoring is a classic example while sentiment analysis of tweets to predict market reactions on certain events is a more recent innovation. Quantification of class probabilities at first sight might just appear to be a technique sub-ordinated to classification. Clearly, classification and quantification are related by calibration issues. This will be discussed in some detail in the context of dataset shift. We will also argue that quantification is a research area in its own right and demonstrate this by examples.
Confirmed
Limit theorems for functionals of excursion sets
Motivated by certain specific geometric characteristics of excursion sets, we shall define local functionals of random fields, and study distributional asymptotics of such functionals in an appropriate setting. Our primary goal is to unearth necessary conditions for ascertaining limiting distributions of scaled sum of local functionals, using various measures of association.
Confirmed
Multivariate Type-G Matérn fields
A new class of non-Gaussian multivariate random fields is formulated using systems of stochastic partial differential equations (SPDEs) with additive spatial type-G noise. We show how to formulate the system to get solutions with marginal Matérn covariance functions for each dimension and derive a parametrization that allows for separate control of cross-covariance and other dependence between the dimensions. Four different constructions of the type-G noise based on normal-variance mixtures are examined. The different constructions result in random fields with increasing flexibility. The fields are incorporated in a geostatistical model with measurement errors and covariates, for which a computationally efficient likelihood-based parameter estimation method is derived.
Confirmed