3 citations · 15 across the 36 of their papers we have counts for
44 papers
Stochastic Knothe-Rosenblatt: Light-speed Calibration of Stochastic Local Volatility Models
Mathias Beiglböck, Manuel Hasenbichler, Gudmund Pammer
European option smiles determine the risk-neutral marginal laws of an asset, but not their intertemporal coupling, which is decisive for many applications. The Bass martingale cons…
A weak transport approach to the Schrödinger-Bass bridge
Manuel Hasenbichler, Gudmund Pammer, Stefan Thonhauser
We study the Schrödinger-Bass problem, a one-parameter family of semimartingale optimal transport problems indexed by , whose limiting regimes interpolate between the classica…
Implicit Regularization of Large Neural Networks via Mean-Field Formulation
Beatrice Acciaio, Jakob Heiss, Gudmund Pammer +1
We propose a mathematical framework to explain implicit regularization from early stopping during the training of overparametrized neural networks. In the mean-field limit, the par…
The geometry of the adapted Bures--Wasserstein space
Beatrice Acciaio, Daniel Bartl, Anne Grass +2
The adapted Bures--Wasserstein space consists of Gaussian processes endowed with the adapted Wasserstein distance. It can be viewed as the analogue of the classical Bures--Wasserst…
Dynamic reinsurance via martingale transport
Beatrice Acciaio, Brandon Garcia Flores, Antonio Marini +1
We formulate a dynamic reinsurance problem in which the insurer seeks to satisfy prescribed terminal moment or risk-based constraints while minimizing the -norm of the ceded r…
On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases
Alexander Korotin, Gudmund Pammer
This paper studies the inverse problem of flow matching (FM) between distributions with finite exponential moment, a problem motivated by modern generative AI applications such as…
A Brenier Theorem on and Applications to Adapted Transport
Mathias Beiglböck, Gudmund Pammer, Stefan Schrott
We develop Brenier theorems on iterated Wasserstein spaces. For a separable Hilbert space and , we construct a full-support probability on $P_2^{N}(H)= P_2(... P_2…
Strassen's theorem for biased convex order
Beatrice Acciaio, Mathias Beiglböck, Evgeny Kolosov +1
Strassen's theorem asserts that for given marginal probabilities there exists a martingale starting in and terminating in if and only if are in convex order. Fr…
Absolutely Continuous Curves of Stochastic Processes
Beatrice Acciaio, Daniel Kršek, Gudmund Pammer +1
We study absolutely continuous curves in the adapted Wasserstein space of filtered processes. We provide a probabilistic representation of such curves as flows of adapted processes…
Estimating causal distances with non-causal ones
Beatrice Acciaio, Songyan Hou, Gudmund Pammer
The adapted Wasserstein () distance refines the classical Wasserstein () distance by incorporating the temporal structure of stochastic processes. This makes the -distan…
The Fundamental Theorem of Weak Optimal Transport
Mathias Beiglböck, Gudmund Pammer, Lorenz Riess +1
The fundamental theorem of classical optimal transport establishes strong duality and characterizes optimizers through a complementary slackness condition. Milestones such as Breni…
The Wasserstein Space of Stochastic Processes in Continuous Time
Daniel Bartl, Mathias Beiglböck, Gudmund Pammer +2
Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the…
Entropic adapted Wasserstein distance on Gaussians
Beatrice Acciaio, Songyan Hou, Gudmund Pammer
The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A com…
The Gradient Flow of the Bass Functional in Martingale Optimal Transport
Julio Backhoff-Veraguas, Gudmund Pammer, Walter Schachermayer
Given and , probability measures on in convex order, a Bass martingale is arguably the most natural martingale starting with law and finishing with law …
Change of numeraire for weak martingale transport
Mathias Beiglböck, Gudmund Pammer, Lorenz Riess
Change of numeraire is a classical tool in mathematical finance. Campi-Laachir-Martini established its applicability to martingale optimal transport. We note that the results of Ca…
Tighter Learning Guarantees on Digital Computers via Concentration of Measure on Finite Spaces
Anastasis Kratsios, A. Martina Neuman, Gudmund Pammer
Machine learning models with inputs in a Euclidean space , when implemented on digital computers, generalize, and their generalization gap converges to at a rate…
Estimating Barycenters of Distributions with Neural Optimal Transport
Alexander Kolesov, Petr Mokrov, Igor Udovichenko +4
Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically ap…
Multicausal transport: barycenters and dynamic matching
Beatrice Acciaio, Daniel Kršek, Gudmund Pammer
We introduce a multivariate version of causal transport, which we name multicausal transport, involving several filtered processes among which causality constraints are imposed. Su…
General duality and dual attainment for adapted transport
Daniel Kršek, Gudmund Pammer
We investigate duality and existence of dual optimizers for several adapted optimal transport problems under minimal assumptions. This includes the causal and bicausal transport, t…
The Knothe-Rosenblatt distance and its induced topology
Mathias Beiglböck, Gudmund Pammer, Alexander Posch
A basic and natural coupling between two probabilities on is given by the Knothe-Rosenblatt coupling. It represents a multiperiod extension of the quantile coupling a…
Representing General Stochastic Processes as Martingale Laws
Mathias Beiglböck, Gudmund Pammer, Stefan Schrott +1
Random variables , are 'probabilistically equivalent' if they have the same law. Moreover, in any class of equivalent random variables it is easy to select canonical r…
Calibration of the Bass Local Volatility model
Beatrice Acciaio, Antonio Marini, Gudmund Pammer
The Bass local volatility model introduced by Backhoff-Veraguas, Beiglböck, Huesmann, and Källblad is a Markov model perfectly calibrated to vanilla options at finitely many maturi…
The Martingale Sinkhorn Algorithm
Manuel Hasenbichler, Benjamin Joseph, Gregoire Loeper +2
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which i…
Energy-Guided Continuous Entropic Barycenter Estimation for General Costs
Alexander Kolesov, Petr Mokrov, Igor Udovichenko +5
Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter tas…