Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

The basic problem of optimal transportation consists in minimizing the expected costs
Ec(X_1,X_2) by varying the joint distribution (X_1,X_2) where the marginal distributions of …

We consider a nondominated model of a discrete-time financial market where stocks are
traded dynamically, and options are available for static hedging. In a general measure …

We study the optimal transport between two probability measures on the real line, where the
transport plans are laws of one-step martingales. A quasi-sure formulation of the dual …

Assume that an agent models a financial asset through a measure ℚ with the goal to
price/hedge some derivative or optimise some expected utility. Even if the model ℚ is …

The Skorokhod embedding problem is to represent a given probability as the distribution of
Brownian motion at a chosen stop** time. Over the last 50 years this has become one of …

A function is exponentially concave if its exponential is concave. We consider exponentially
concave functions on the unit simplex. In a previous paper, we showed that gradient maps of …

We develop computational methods for solving the martingale optimal transport (MOT)
problem—a version of the classical optimal transport with an additional martingale constraint …

We study representations of data from an arbitrary metric space χ in the space of univariate
Gaussian mixtures equipped with a transport metric (Delon and Desolneux 2020). We prove …

A number of researchers have introduced topological structures on the set of laws of
stochastic processes. A unifying goal of these authors is to strengthen the usual weak …