At Erasmus Universiteit Rotterdam (March 28, 2024)

## 11:00-11:45 Juan Juan Cai (Vrije Universiteit Amsterdam)

**Title**: Risk of Extreme Accounting Failures

**Abstract**: We use extreme value theory to estimate the risk of extreme accounting failures using U.S. restatement data over the period 1995-2022. This risk has as yet rarely been quantified, even though its reduction is a commonly cited policy objective in financial reporting regulation. Although we find that the Value-at-Risk has been halved after the introduction of the Sarbanes-Oxley act, extreme financial restatement risk on the U.S. stock market remains substantial: the estimated 1-year probability of a more than $1bn downward correction in net income is still close to 40%.

This is a joint work with Kees Camfferman, Andre Lucas and Jacco L. Wielhouwer

## Lunch Break

## 12:00-13:00 Anja Jansen (Otto-von-Guericke-Universität Magdeburg)

**Title**: Metric embeddings of tail correlation matrices

**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).