Financial and actuarial risk assessment is typically based on the computation of a single quantile (or Value-at-Risk). One drawback of quantiles is that they only take into account the frequency of an extreme event, and in particular do not give an idea of what the typical magnitude of such an event would be. Another issue is that they do not induce a coherent risk measure, which is a serious concern in actuarial and financial applications. In this talk, I will explain how, starting from the formulation of a quantile as the solution of an optimisation problem, one may come up with two alternative families of risk measures, called expectiles and extremiles. I will give a broad overview of their properties, as well as of their estimation at extreme levels in heavy-tailed models, and explain why they constitute sensible alternatives for risk assessment using some real data applications. This is based on joint work with Abdelaati Daouia, Irène Gijbels, Stéphane Girard and Antoine Usseglio-Carleve.
The talk will give an overview of what Gilles Stupfler has been working on in the past few years. The main two underlying papers can be found at https://doi.org/10.1111/rssb.12254 and https://doi.org/10.1080/01621459.2018.1498348
Personal website of Gilles Stupfler
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