21 citations · 48 across the 18 of their papers we have counts for
22 papers
Hopf-Lax approximation for value functions of Lévy optimal control problems
Michael Kupper, Max Nendel, Alessandro Sgarabottolo
In this paper, we investigate stochastic versions of the Hopf-Lax formula which are based on compositions of the Hopf-Lax operator with the transition kernel of a Lévy process taki…
Risk measures based on weak optimal transport
Michael Kupper, Max Nendel, Alessandro Sgarabottolo
In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a non…
Convergence of infinitesimal generators and stability of convex monotone semigroups
Jonas Blessing, Michael Kupper, Max Nendel
Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of cont…
An axiomatic approach to default risk and model uncertainty in rating systems
Max Nendel, Jan Streicher
In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), a…
A parametric approach to the estimation of convex risk functionals based on Wasserstein distance
Max Nendel, Alessandro Sgarabottolo
In this paper, we explore a static setting for the assessment of risk in the context of mathematical finance and actuarial science that takes into account model uncertainty in the…
Lower semicontinuity of monotone functionals in the mixed topology on
Max Nendel
The main result of this paper characterizes the continuity from below of monotone functionals on the space of bounded continuous functions on an arbitrary Polish space as low…
Operator semigroups in the mixed topology and the infinitesimal description of Markov processes
Ben Goldys, Max Nendel, Michael Röckner
We define a class of not necessarily linear -semigroups on (more generally, on , for some bounded function , which is the p…
Convex monotone semigroups and their generators with respect to -convergence
Jonas Blessing, Robert Denk, Michael Kupper +1
We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to -convergence. In contrast to the linear theory, the domain…
A unifying framework for submodular mean field games
Jodi Dianetti, Giorgio Ferrari, Markus Fischer +1
We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field…
Wasserstein perturbations of Markovian transition semigroups
Sven Fuhrmann, Michael Kupper, Max Nendel
In this paper, we deal with a class of time-homogeneous continuous-time Markov processes with transition probabilities bearing a nonparametric uncertainty. The uncertainty is model…
Convex monotone semigroups on lattices of continuous functions
Robert Denk, Michael Kupper, Max Nendel
We consider convex monotone -semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a -Dedekind complete Banach lattice. Typical examples include the sp…
Separability vs. robustness of Orlicz spaces: financial and economic perspectives
Felix-Benedikt Liebrich, Max Nendel
We investigate robust Orlicz spaces as a generalisation of robust -spaces. Two constructions of such spaces are distinguished, a top-down approach and a bottom-up approach. We…
A decomposition of general premium principles into risk and deviation
Max Nendel, Frank Riedel, Maren Diane Schmeck
We provide an axiomatic approach to general premium principles in a probability-free setting that allows for Knightian uncertainty. Every premium principle is the sum of a risk mea…
A note on stochastic dominance and compactness
Max Nendel
In this work, we discuss completeness for the lattice orders of first and second order stochastic dominance. The main results state that, both, first and second order stochastic do…
Convex semigroups on -like spaces
Robert Denk, Michael Kupper, Max Nendel
In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having -spaces in mind as a typical application. We show that the basic results…
Submodular Mean Field Games: Existence and Approximation of Solutions
Jodi Dianetti, Giorgio Ferrari, Markus Fischer +1
We study mean field games with scalar It{ô}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity…
Upper envelopes of families of Feller semigroups and viscosity solutions to a class of nonlinear Cauchy problems
Max Nendel, Michael Röckner
In this paper, we consider the (upper) semigroup envelope, i.e. the least upper bound, of a given family of linear Feller semigroups. We explicitly construct the semigroup envelope…
Regularity and asymptotic behaviour for a damped plate-membrane transmission problem
Bienvenido Barraza Martinez, Robert Denk, Jairo Hernandez Monzon +2
We consider a transmission problem where a structurally damped plate equation is coupled with a damped or undamped wave equation by transmission conditions. We show that exponentia…
Markov chains under nonlinear expectation
Max Nendel
In this paper, we consider continuous-time Markov chains with a finite state space under nonlinear expectations. We define so-called Q-operators as an extension of Q-matrices or ra…
A semigroup approach to nonlinear Lévy processes
Robert Denk, Michael Kupper, Max Nendel
We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinea…
Mapping properties for operator-valued pseudodifferential operators on toroidal Besov spaces
Bienvenido Barraza Martínez, Robert Denk, Jairo Hernández Monzón +1
In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without as…
Kolmogorov type and general extension results for nonlinear expectations
Robert Denk, Michael Kupper, Max Nendel
We provide extension procedures for nonlinear expectations to the space of all bounded measurable functions. We first discuss a maximal extension for convex expectations which have…