Séminaire du CIMMUL-Quantact | Max Nendel

Upper Comonotonicity and Risk Aggregation under Dependence Uncertainty

Max Nendel
University of Waterloo

Résumé

In this talk, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal couplings, as a generalization of well-known correlation statistics such as the Pearson correlation. The first main result states that even an arbitrarily small positive dependence between losses can result in perfectly correlated tails beyond a certain threshold and seemingly complete independence before this threshold. In a second step, we focus on the aggregation of individual risks with known marginal distributions by means of arbitrary nondecreasing left-continuous aggregation functions. In this context, we show that under an arbitrarily small positive dependence, the tail risk of the aggregate loss might coincide with the one of perfectly correlated losses. A similar result is derived for expectiles under mild conditions. In a last step, we discuss our results in the context of credit risk, analyzing the potential effects on the value at risk for weighted sums of Bernoulli distributed losses.

The talk is based on joint work with Corrado De Vecchi and Jan Streicher.

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Le séminaire aura lieu au local 3820 du pavillon Alexandre-Vachon et en ligne.

Pour rejoindre la réunion Zoom :
https://ulaval.zoom.us/j/62680136430?pwd=eldBYjdNTG5QR2VxTTFqbVM4UGVRZz09

Meeting ID: 626 8013 6430
Passcode: 693150