# Graduate Crash Course on Risk Measures

Tomorrow morning, I will give a crash course on risk measures at Louvain-la-Neuve, in Belgium. This is a crash course of PhD students (and researchers) with a long introduction on the univariate static framework (and some mathematical tools that will be interesting later on, such as the Fenchel transform and more generally on convexity, as well as some results on optimal transport). I will also mention what was obtained in decision theory, inspired by Itzhak Gilboa‘s Theory of Decision under Uncertainty. Then I will mention extensions to derive multiple risk measures, based on Marc Henry and Alfred Galichon‘s work. Finally, I will conclude by introducing the difficulty to derive dynamic risk measures.

The slides are based on a document I am still working on. And unfortunately, the deeper I get to explain the roots of the axioms, or the assumptions, the more papers I discover (and I need to read, and understand). So I guess I will need some time to finalize my survey. Note that I decided to skip details on technical issues when working on $L^\infty$, and the weak topology on the dual of $L^\infty$. I will try to add additional references in the notes, but I wanted the slides to be as simple as possible. I also want to add more connections with statistical results, such as Neyman Pearson’s lemma, for instance (as mentioned in a paper by Alexander Schied). All my apologies for the typos, too.

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