158 citations · 363 across the 23 of their papers we have counts for
13 papers · 1 filter
A Probabilistic View on the Adapted Wasserstein Distance
Mathias Beiglböck, Susanne Pflügl, Stefan Schrott
Causal optimal transport and adapted Wasserstein distance have applications in different fields from optimization to mathematical finance and machine learning. The goal of this art…
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…
The most exciting game
Julio Backhoff-Veraguas, Mathias Beiglboeck
Motivated by a problem posed by Aldous, our goal is to find the maximal-entropy win-martingale: In a sports game between two teams, the chance the home team wins is initially $x_0…
Denseness of biadapted Monge mappings
Mathias Beiglböck, Gudmund Pammer, Stefan Schrott
Adapted or causal transport theory aims to extend classical optimal transport from probability measures to stochastic processes. On a technical level, the novelty is to restrict to…
The Wasserstein space of stochastic processes
Daniel Bartl, Mathias Beiglböck, Gudmund Pammer
Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous a…
Shadow couplings
Mathias Beiglboeck, Nicolas Juillet
A classical result of Strassen asserts that given probabilities on the real line which are in convex order, there exists a \emph{martingale coupling} with these marginals, i…
A land of monotone plenty
Mathias Beiglböck, Claus Griessler
A fundamental concept in optimal transport is c-cyclical monotonicity: it allows to link the optimality of transport plans to the geometry of their support sets. Recently, related…
Martingale Inequalities and Deterministic Counterparts
Mathias Beiglböck, Marcel Nutz
We study martingale inequalities from an analytic point of view and show that a general martingale inequality can be reduced to a pair of deterministic inequalities in a small numb…
Optimal Transport and Skorokhod Embedding
Mathias Beiglboeck, Alexander M. G. Cox, Martin Huesmann
The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of…
Pathwise versions of the Burkholder-Davis-Gundy inequality
Mathias Beiglböck, Pietro Siorpaes
We present a new proof of the Burkholder-Davis-Gundy inequalities for . The novelty of our method is that these martingale inequalities are obtained as consequences…
On a problem of optimal transport under marginal martingale constraints
Mathias Beiglböck, Nicolas Juillet
The basic problem of optimal transportation consists in minimizing the expected costs by varying the joint distribution where the marginal dis…
A trajectorial interpretation of Doob's martingale inequalities
B. Acciaio, M. Beiglböck, F. Penkner +2
We present a unified approach to Doob's maximal inequalities for . The novelty of our method is that these martingale inequalities are obtained as consequence…
A Direct Proof of the Bichteler--Dellacherie Theorem and Connections to Arbitrage
Mathias Beiglböck, Walter Schachermayer, Bezirgen Veliyev
We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes allowing for a useful integration theory consist…