158 citations · 363 across the 23 of their papers we have counts for
26 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…
Adapted Law Invariance and Time-Consistent Dynamic Risk Measures
Mathias Beiglböck, Silvana M. Pesenti, Maxime Sylvestre
In static risk measurement, law invariance expresses the principle that the risk of a position should depend only on its distribution, and not on the particular probability space o…
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…
Evidence suggests that SARS-CoV-2 rapid antigen tests provide benefits for epidemic control -- observations from Austrian schools
Jitka Polechová, Kory D. Johnson, Pavel Payne +4
Rapid antigen tests detect proteins at the surface of virus particles, identifying the disease during its infectious phase. In contrast, PCR tests detect viral genomes; they can th…
A non-linear monotonicity principle and applications to Schrödinger type problems
Julio Backhoff-Veraguas, Mathias Beiglböck, Giovanni Conforti
A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar…
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…
Model-independent Bounds for Option Prices: A Mass Transport Approach
Mathias Beiglböck, Pierre Henry-Labordère, Friedrich Penkner
In this paper we investigate model-independent bounds for exotic options written on a risky asset. Based on arguments from the theory of Monge-Kantorovich mass-transport we establi…
Utility Maximization, Risk Aversion, and Stochastic Dominance
Mathias Beiglboeck, Johannes Muhle-Karbe, Johannes Temme
Consider an investor trading dynamically to maximize expected utility from terminal wealth. Our aim is to study the dependence between her risk aversion and the distribution of the…
Duality for rectified Cost Functions
Mathias Beiglboeck, Aldo Pratelli
It is well-known that duality in the Monge-Kantorovich transport problem holds true provided that the cost function is lower semi-continuous or finitely…
A generalized dual maximizer for the Monge--Kantorovich transport problem
Mathias Beiglböck, Christian Léonard, Walter Schachermayer
The dual attainment of the Monge--Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability mea…
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…
Is the minimum value of an option on variance generated by local volatility?
Mathias Beiglboeck, Peter Friz, Stephan Sturm
We discuss the possibility of obtaining model-free bounds on volatility derivatives, given present market data in the form of a calibrated local volatility model. A counter-example…
Transfinite Approximation of Hindman's Theorem
Mathias Beiglböck, Henry Towsner
Hindman's Theorem states that in any finite coloring of the integers, there is an infinite set all of whose finite sums belong to the same color. This is much stronger than the cor…
On the Duality Theory for the Monge--Kantorovich Transport Problem
Mathias Beiglboeck, Christian Leonard, Walter Schachermayer
The paper is accompanying "A general Duality Theorem for the Monge-Kantorovich Transport Problem". We explain the methods used in this article in an elementary setting and present…