Coherent and law-invariant risk measures

par Laurent Pfeiffer

vendredi 7 nov. 2025, 11:00 → 11:30 Europe/Paris

XR203 (XLIM)

In order to evaluate and optimize a random cost, the expectation is often an unsatisfactory tool, in so far as it does not take into account the aversion that one may have towards the variability of the cost of interest. Risk measures allow us to model this form of aversion; a classical example is the conditional value at risk.

 

In this talk, we will focus on coherent and law-invariant risk measures. I will first present a new characterization of these, based on a particular optimal transport problem. We will use it to derive novel dual representations of risk measures. In the second part of the talk, I will show how to formulate stochastic optimal control problems with risk measures as mean-field optimal control problem and discuss some possible numerical approaches.