In this talk, we will present two main results in our study of distributionally robust risk measures (a.k.a. worst-case risk measures), where the largest risk level needs to be estimated in the case that only on the mean and variance information is available. We show that the problem can be boiled down to a closed-form expression for any (law invariant) coherent risk measure, and most importantly, the worst-case distributions giving the largest risk estimate can be fully characterized by distributions bounded from below. In particular, the worst-case distributions are coherent in their representation of one’s subjective risk aversion and hence, they provide convincing intuition for the usefulness of distributionally robust risk measures.
Bienvenue à tous!