Michael Kupper

Representation Theorems for Convex Expectations and Semigroups on Path Space

The objective of this paper is to investigate the connection between penalty functions from stochastic optimal control, convex semigroups from analysis, and convex expectations from probability theory. Our main result provides a one-to-one relation between these objects. As an ap...

Martingales and path-dependent PDEs via evolutionary semigroups

Abstract In this article, we develop a semigroup-theoretic framework for the analytic characterization of martingales with path-dependent terminal conditions. Our main result establishes that a measurable adapted process of the form $$ V(t) - \int _0^t \Psi (s)\, ds $$ V ( t ) -...