3 citations · 15 across the 36 of their papers we have counts for
29 papers · 1 filter
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…
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…
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…
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…
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…
An extension of martingale transport and stability in robust finance
Benjamin Jourdain, Gudmund Pammer
While many questions in robust finance can be posed in the martingale optimal transport framework or its weak extension, others like the subreplication price of VIX futures, the ro…
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…
A regularized Kellerer theorem in arbitrary dimension
Gudmund Pammer, Benjamin A. Robinson, Walter Schachermayer
We present a multidimensional extension of Kellerer's theorem on the existence of mimicking Markov martingales for peacocks, a term derived from the French for stochastic processes…
Lipschitz continuity of the Wasserstein projections in the convex order on the line
Benjamin Jourdain, William Margheriti, Gudmund Pammer
Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequa…
A short proof of the characterisation of convex order using the 2-Wasserstein distance
Beatrice Acciaio, Gudmund Pammer
We provide a short proof of the intriguing characterisation of the convex order given by Wiesel and Zhang.
A note on the adapted weak topology in discrete time
Gudmund Pammer
The adapted weak topology is an extension of the weak topology for stochastic processes designed to adequately capture properties of underlying filtrations. With the recent work of…
Computational methods for adapted optimal transport
Stephan Eckstein, Gudmund Pammer
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In t…
Faking Brownian motion with continuous Markov martingales
Mathias Beiglböck, George Lowther, Gudmund Pammer +1
Hamza-Klebaner posed the problem of constructing martingales with Brownian marginals that differ from Brownian motion, so called fake Brownian motions. Besides its theoretical appe…
Stability of the Weak Martingale Optimal Transport Problem
Mathias Beiglböck, Benjamin Jourdain, William Margheriti +1
While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also non-linear cost functionals. Following th…
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…