• Graduate Program
    • Why study Business Data Science?
    • Program Outline
    • Courses
    • Course Registration
    • Admissions
    • Facilities
  • Research
  • News
  • Summer School
    • Deep Learning
    • Machine Learning for Business
    • Tinbergen Institute Summer School Program
    • Receive updates
  • Events
    • Events Calendar
    • Events archive
    • Summer school
      • Deep Learning
      • Machine Learning for Business
      • Tinbergen Institute Summer School Program
      • Receive updates
    • Tinbergen Institute Lectures
    • Annual Tinbergen Institute Conference archive
  • Alumni
Home | Events Archive | Metric embeddings of tail correlation matrices
Seminar

Metric embeddings of tail correlation matrices


  • Series
    Erasmus Econometric Institute Series
  • Speakers
    Anja Janssen (Otto-von-Guericke-University Magdeburg, Germany)
  • Field
    Econometrics
  • Location
    Erasmus University Rotterdam, E building, room ET-14
    Rotterdam
  • Date and time

    March 28, 2024
    12:00 - 13:00

Abstract
The assessment of risks associated with multivariate random vectors relies heavily on understanding their extremal dependence, crucial in evaluating risk measures for financial or insurance portfolios. A widely used metric for assessing tail risk is the tail correlation matrix of tail correlation coefficients. Among the exploration of structural properties of the tail correlation matrix the so-called realization problem of deciding whether a given matrix is the tail correlation matrix of some underlying random vector has recently received some attention.

The entries of the tail correlation matrix are closely related to a useful distance measure on the space of Frechet-random variables, named spectral distance and first introduced in Davis & Resnick (1993). We analyze the properties of a related semimetric and show that it has the special property of being embeddable both in vector and function space, equipped with the respective sum norm. Notably, these embeddings bear a direct relationship with the realization of specific tail dependence structures via max-stable random vectors. Particularly, an embedding in vector space, employing so-called line metrics, provides a representation through a max-stable mixture of so-called Tawn-Molchanov models, s. also Fiebig, Strokorb & Schlather (2017).

Leveraging this framework, we revisit the realization problem, affirming a conjecture by Shyamalkumar & Tao (2020) regarding its NP-completeness.

This talk is based on joint work with Sebastian Neblung (University of Hamburg) and Stilian Stoev (University of Michigan).