Carole Bernard (Vrije Universiteit Brussels, Belgium)

Title:  Robust Risk Management

Making sound decisions under uncertainty generally requires quantitative analysis and the use of models. However, a “perfect” model does not exist since some divergence between the model and the reality it attempts to describe cannot be avoided. In a broad sense, model risk is about the extent to which the quality of model-based decisions is sensitive to underlying model deviations and data issues.

An example concerns the establishment of the capital buffers banks need to put aside to absorb unforeseen losses for a portfolio of risky loans. Doing so requires accurate estimates of the likelihood that various obligors default together, which is very difficult due to a scarcity of data.

We will discuss various approaches on how to plan for worst-case scenarios in a financial and insurance context.  More specifically, we will discuss the problem of quantifying model uncertainty, such as departures from assumed independence, incomplete dependence information, factor models that are only partially specified, or portfolio information that is only available on an aggregate level (e.g., mean and variance of the portfolio loss), desired properties (e.g., unimodality, symmetry, non-negativity).

We will develop necessary tools to quantify this model uncertainty and in particular to determine the best upper and lower risk bounds for various risk aggregation functionals of interest including Value-at-Risk, Range Value-at-Risk and distorted risk measures. The short course is based on the cited recent book and papers below.

References:

L. Rüschendorf , S. Vanduffel, C. Bernard. Model Risk Management: Risk Bounds under Uncertainty. Cambridge University Press; 2024. 

C. Bernard, S. Pesenti , S. Vanduffel. Robust Distortions Measures. 2023, Mathematical Finance, forthcoming, available at SSRN, published in an open access.

C. Bernard, A. Müller (University of Siegen) and M. Oesting. Lp-norm spherical copulas, Journal of Multivariate Analysis, 2023, forthcoming, arXiv:2206.10180.

C. Bernard, C. De Vecchi, S. Vanduffel. Impact of Correlation on the (Range) Value-at-Risk. 2023, Scandinavian Actuarial Journal , (6), 531–564, published version.

C. Bernard, R. Kazzi , S. Vanduffel. Range Value-at-Risk Bounds for Unimodal Distributions under Partial Information. 2020, Insurance: Mathematics and Economics, 94, 9-24, published version, available at SSRN.

C. Bernard, O. Bondarenko (UIC) and S. Vanduffel. Rearrangement Algorithm and Maximum Entropy. 2018, Annals of Operational Research, 261(1-2), 107-134, PDF in open access, available at SSRN.

C. Bernard, L. Rüschendorf , S. Vanduffel, R. Wang. Risk bounds for factor models. 2017, Finance and Stochastics , 21(3), 631-659, published version, available at SSRN.

C. Bernard, L. Rüschendorf , S. Vanduffel. VaR Bounds with Variance Constraint. 2017, Journal of Risk and Insurance , 84(3), 923-959, published version, available at SSRN.

C. Bernard, X. Jiang and R. Wang. Risk Aggregation with Dependence Uncertainty. 2014, Insurance: Mathematics and Economics , 54, 93-108, published version.