11 papers
Extreme points of sets of probability measures and -divergences
Gerrit Bauch, Max Nendel, Alessandro Sgarabottolo
In this work, we prove several equivalent characterizations of the extreme points of convex sets of probability measures of the form , where $\mathc…
A Small-Noise Analysis of Controlled Functional Differential Equations with Gaussian Noise
David Criens, Max Nendel
We study small-noise asymptotics for controlled functional differential equations driven by additive Gaussian noise. The Gaussian noise is modeled on an abstract Wiener space, cove…
Optimal Market Making in Prediction Markets
Dominik Feil, Max Nendel
Prediction markets are attracting growing attention as trading volumes rise and their practical relevance increases. To ensure efficient price discovery, liquidity provision become…
An optimal transport foundation for a class of dynamically consistent risk measures
Sven Fuhrmann, Michael Kupper, Max Nendel
We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition la…
Asymptotic Behaviour of Unexpected Losses and Risk Ratios for Co-Monotonic Alternatives
Max Nendel
The aggregation of individual risks in large credit and insurance portfolios is guided by diversification and the law of large numbers, which formalizes the convergence of sample a…
A Strict Comparison Principle for Integro-Differential Hamilton-Jacobi-Bellman Equations on Domains with Boundary
Serena Della Corte, Fabian Fuchs, Richard C. Kraaij +1
This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test…
Chernoff-Mehler Approximation for Lévy Processes with Drift
Max Nendel
In this paper, we study an approximation scheme for Lévy processes with drift in terms of a representation that is akin to the celebrated Mehler formula for Lévy-Ornstein-Uhlenbeck…
Scaling limits of multi-period distributionally robust optimization problems
Max Nendel, Ariel Neufeld, Kyunghyun Park +1
We examine the scaling limit of multi-period distributionally robust optimization (DRO) problems via a semigroup approach. Each period involves a worst-case maximization over distr…
Existence of Viscosity Solutions to Abstract Cauchy Problems via Nonlinear Semigroups
Fabian Fuchs, Max Nendel
In this work, we provide conditions for nonlinear monotone semigroups on locally convex vector lattices to give rise to a generalized notion of viscosity solutions to a related non…
Pasting of Equilibria and Donsker-type Results for Mean Field Games
Jodi Dianetti, Max Nendel, Ludovic Tangpi +1
This paper studies the relation between equilibria in single-period, discrete-time and continuous-time mean field game models. First, for single-period mean field games, we establi…
A comparison principle based on couplings of partial integro-differential operators
Serena Della Corte, Fabian Fuchs, Richard C. Kraaij +1
This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial inte…