Actuarial Science and Financial Mathematics seminar seriesÂ
Michael Kupper
University of Konstanz
Room: M3 3127
Risk measures based on weak optimal transport and approximation of drift control problems
We discuss convex risk measures with weak optimal transport penalties and show that these risk measures admit an explicit representation via a nonlinear transform of the loss function. We discuss several examples, including classical optimal transport penalties and martingale constraints. In the second part of the talk, we focus on the composition of related functionals. We consider a stochastic version of the Hopf–Lax formula, where the Hopf–Lax operator is composed with the transition kernel of a Lévy process. We show that, depending on the order of composition, one obtains upper and lower bounds for the value function of a stochastic optimal control problem associated with drift-controlled Lévy dynamics. The value function of the control problem is approximated both from above and below as the number of iterations tends to infinity, and we provide explicit convergence rates for the approximation procedure.
The talk is based on joint work with Max Nendel and Alessandro Sgarabottolo.